id large_stringlengths 9 16 | title large_stringlengths 1 382 | abstract large_stringlengths 3 6.09k | publish_date date32 | update_date date32 | categories large listlengths 1 13 | authors large_stringlengths 3 62.8k |
|---|---|---|---|---|---|---|
math/9404214 | Polynomial Grothendieck properties | A Banach space $E$ has the Grothendieck property if every (linear bounded)
operator from $E$ into $c_0$ is weakly compact. It is proved that, for an
integer $k>1$, every $k$-homogeneous polynomial from $E$ into $c_0$ is weakly
compact if and only if the space ${\cal P}(^kE)$ of scalar valued polynomials
on $E$ is refle... | 1994-04-25 | 2016-09-06 | [
"math.FA"
] | Manuel Gonzalez, Joaquin M. Gutierrez |
math/9404212 | A Banach subspace of $L_{1/2}$ which does not embed in $L_1$ (isometric
version) | For every $n\geq 3,$ we construct an $n$-dimensional Banach space which is
isometric to a subspace of $L_{1/2}$ but is not isometric to a subspace of
$L_1.$ The isomorphic version of this problem (posed by S. Kwapien in 1969) is
still open. Another example gives a Banach subspace of $L_{1/4}$ which does not
embed isome... | 1994-04-20 | 2016-09-06 | [
"math.FA"
] | Alexander Koldobsky |
math/9404213 | Subspaces containing biorthogonal functionals of bases of different
types | The paper is devoted to two particular cases of the following general
problem. Let $\alpha$ and $\beta$ be two types of bases in Banach spaces. Let a
Banach space $X$ has bases of both types and a subspace $M\subset X^*$ contains
the sequence of biorthogonal functionals of some $\alpha$-basis in $X$. Does
$M$ contain a... | 1994-04-20 | 2010-09-07 | [
"math.FA"
] | Mikhail I. Ostrovskii |
math/9404211 | Representing non-weakly compact operators | For each $S \in L(E)$ (with $E$ a Banach space) the operator $R(S) \in
L(E^{**}/E)$ is defined by $R(S)(x^{**}+E) = S^{**}x^{**}+E$ \quad ($x^{**}\in
E^{**}$). We study mapping properties of the correspondence $S\to R(S),$ which
provides a representation $R$ of the weak Calkin algebra $L(E)/W(E)$ (here
$W(E)$ denotes t... | 1994-04-14 | 2016-09-06 | [
"math.FA"
] | Manuel Gonzalez, Eero Saksman, H. Tylli |
math/9404210 | Orlicz property of operator spaces and eigenvalue estimates | As is well known absolute convergence and unconditional convergence for
series are equivalent only in finite dimensional Banach spaces. Replacing the
classical notion of absolutely summing operators by the notion of 1 summing
operators \[ \summ_k || Tx_k || \leq c || \summ_k e_k \otimes x_k
||_{\ell_1\otimes_{min}E}\] ... | 1994-04-14 | 2016-09-06 | [
"math.FA"
] | Marius Junge |
math/9404209 | Factorization and Reflexivity on Fock spaces | The framework of the paper is that of the full Fock space ${\Cal F}^2({\Cal
H}_n)$ and the Banach algebra $F^\infty$ which can be viewed as non-commutative
analogues of the Hardy spaces $H^2$ and $H^\infty$ respectively.
An inner-outer factorization for any element in ${\Cal F}^2({\Cal H}_n)$ as
well as characterizat... | 1994-04-14 | 2016-09-06 | [
"math.FA"
] | Alvaro Arias, Gelu Popescu |
math/9404207 | Real and complex operator ideals | The powerful concept of an operator ideal on the class of all Banach spaces
makes sense in the real and in the complex case. In both settings we may, for
example, consider compact, nuclear, or $2$--summing operators, where the
definitions are adapted to each other in a natural way. This paper deals with
the question wh... | 1994-04-12 | 2016-09-06 | [
"math.FA"
] | Joerg Wenzel |
math/9404208 | Ideal norms and trigonometric orthonormal systems | In this article, we characterize the $UMD$--property of a Banach space $X$ by
ideal norms associated with trigonometric orthonormal systems.
The asymptotic behavior of that numerical parameters can be used to decide
whether or not $X$ is a $UMD$--space. Moreover, in the negative case, we obtain
a measure that shows h... | 1994-04-12 | 2016-09-06 | [
"math.FA"
] | Joerg Wenzel |
math/9404234 | A subsequence principle characterizing Banach spaces containing $c_0$ | The notion of a strongly summing sequence is introduced. Such a sequence is
weak-Cauchy, a basis for its closed linear span, and has the crucial property
that the dual of this span is not weakly sequentially complete. The main result
is:
Theorem. Every non-trivial weak-Cauchy sequence in a \RM(real or complex\RM)
Ban... | 1994-04-01 | 2016-09-06 | [
"math.FA",
"math.LO"
] | Haskell Rosenthal |
math/9403212 | Classes of Banach spaces stable and unstable with respect to the opening | The paper is a complement to the survey: M.I.Ostrovskii "To\-po\-lo\-gies on
the set of all subspaces of a Banach space and related questions of Banach
space geometry", Quaestiones Math. (to appear). It contains proofs of some
results on stability of properties of Banach spaces with respect to the
geometric opening sta... | 1994-03-31 | 2010-09-07 | [
"math.FA"
] | Mikhail I. Ostrovskii |
math/9403211 | New proofs of Rosenthal's $\ell^{1}$--theorem and the
Josefson--Nissenzweig theorem | We give elementary proofs of the theorems mentioned in the title. Our methods
rely on a simple version of Ramsey theory and a martingale difference lemma.
They also provide quantitative results: if a Banach space contains $\ell^{1}$
only with a bad constant then every bounded sequence admits a subsequence which
is ``ne... | 1994-03-31 | 2016-09-06 | [
"math.FA"
] | Ehrhard Behrends |
math/9403210 | Self-Induced Compactness in Banach Spaces | The question which led to the title of this note is the following:
{\it If $X$ is a Banach space and $K$ is a compact subset of $X$, is it
possible to find a compact, or even approximable, operator $v:X\to X$ such that
$K\subset\ol{v(B_X)}$?}
This question was first posed by P.G.Dixon [6] in connection with
investi... | 1994-03-28 | 2016-09-06 | [
"math.FA"
] | Peter G. Casazza, Hans Jarchow |
math/9403208 | Asymptotic infinite-dimensional theory of Banach spaces | In this paper structure of infinite dimensional Banach spaces is studied by
using an asymptotic approach based on stabilization at infinity of finite
dimensional subspaces which appear everywhere far away. This leads to notions
of asymptotic structures and asymptotic versions of a given Banach space. As an
example of a... | 1994-03-28 | 2016-09-06 | [
"math.FA"
] | Bernard Maurey, Vitali D. Milman, Nicole Tomczak-Jaegermann |
math/9403209 | Quojections without Banach subspaces | A quojection (projective limit of Banach spaces with surjective linking
mappings) without infinite dimensional Banach subspaces is constructed. This
results answers a question posed by G.Metafune and V.B.Moscatelli. | 1994-03-28 | 2010-09-07 | [
"math.FA"
] | Mikhail I. Ostrovskii |
math/9403207 | Contractive projections and isometries in sequence spaces | We characterize 1-complemented subspaces of finite codimension in strictly
monotone one-$p$-convex, $2<p<\infty,$ sequence spaces. Next we describe, up to
isometric isomorphism, all possible types of 1-unconditional structures in
sequence spaces with few surjective isometries. We also give a new example of a
class of r... | 1994-03-04 | 2016-09-06 | [
"math.FA"
] | Beata Randrianantoanina |
math/9403206 | Banach spaces with the $2$-summing property | A Banach space $X$ has the $2$-summing property if the norm of every linear
operator from $X$ to a Hilbert space is equal to the $2$-summing norm of the
operator. Up to a point, the theory of spaces which have this property is
independent of the scalar field: the property is self-dual and any space with
the property is... | 1994-03-02 | 2016-09-06 | [
"math.FA"
] | Alvaro Arias, Tadek Figiel, William B. Johnson, Gideon Schechtman |
math/9403205 | The Banach space $H^1(X,d,\mu)$, II | In this paper we give the isomorphic classification of atomic $H^1(X,d,\mu)$,
where $(X,d,\mu)$ is a space of homogeneous type, hereby completing a line of
investigation opened by the work of Bernard Maurey [Ma1], [Ma2], [Ma3] and
continued by Lennard Carleson [C] and Przemyslaw Wojtaszczyk [Woj1], [Wpj2]. | 1994-03-02 | 2016-09-06 | [
"math.FA"
] | Paul F. X. M\"uller |
math/9402211 | Isomorphisms of operator algebras | In this paper we prove that several operator algebras are completely
isomorphic to each other; e.g., the $C^*_\lambda(F_k)$, $k\geq 2$, the
$C^*$-algebras generated by the regular left representation $\lambda:F_k\to
B(\ell_2(F_k))$, are completely isomorphic to each other.
We also study the ``non-commutative'' analyt... | 1994-02-21 | 2008-02-03 | [
"math.FA"
] | Alvaro Arias |
math/9402210 | From weak to strong types of $L_E^1$-convergence by the Bocce-criterion | Necessary and sufficient oscillation conditions are given for a weakly
convergent sequence (resp. relatively weakly compact set) in the
Bochner-Lebesgue space $\l1$ to be norm convergent (resp. relatively norm
compact), thus extending the known results for $\rl1$. Similarly, necessary and
sufficient oscillation conditi... | 1994-02-17 | 2016-09-06 | [
"math.FA"
] | Erik J. Balder, Maria Girardi, Vincent Jalby |
math/9402207 | An elementary example of a Banach space not isomorphic to its complex
conjugate | We give a simple and explicit example of a complex Banach space which is not
isomorphic to its complex conjugate, and hence of two real-isomorphic spaces
which are not complex-isomorphic. | 1994-02-11 | 2008-02-03 | [
"math.FA"
] | Nigel J. Kalton |
math/9402209 | Nest algebras in $c_1$ | In this paper we address some basic questions of the Banach space structure
of the nest algebras in the trace class; in particular, we study whether any
two of them are isomorphic to each other, and show that the nest algebras in
the trace class have bases. We construct three non-isomorphic examples of nest
algebras in... | 1994-02-11 | 2009-09-25 | [
"math.FA"
] | Alvaro Arias |
math/9402206 | Complex interpolation of Hardy-type subspaces | We consider the problem of complex interpolation of certain Hardy-type
subspaces of K\"othe function spaces. For example, suppose $X_0$ and $X_1$ are
K\"othe function spaces on the unit circle $\bold T,$ and let $H_{X_0}$ and
$H_{X_1}$ be the corresponding Hardy spaces. Under mild conditions on $X_0,X_1$
we give a nece... | 1994-02-11 | 2016-09-06 | [
"math.FA"
] | Nigel J. Kalton |
math/9402208 | Embedding Orlicz Sequence Spaces into $C(\alpha)$ | Let $M$ be a non-degenerate Orlicz function such that there exist $\ep > 0$
and $0 < s < 1$ with $\su M(\ep s^i)/M(s^i) < \infty$. It is shown that the
Orlicz sequence space $h_M$ is isomorphic to a subspace of $C(\om^\om)$. It is
also shown that for any non-degenerate Orlicz function $M$, $h_M$ does not
embed into $C(... | 1994-02-11 | 2008-02-03 | [
"math.FA"
] | Denny H. Leung |
math/9402205 | On the structure of tensor products of l_p spaces | We examine some structural properties of (injective and projective) tensor
products of $\ell_p$-spaces (projections, complemented subspaces, reflexivity,
isomorphisms, etc.). We combine these results with combinatorial arguments to
address the question of primarity for these spaces and their duals.
Our main results a... | 1994-02-08 | 2016-09-06 | [
"math.FA"
] | Alvaro Arias, Jeff Farmer |
math/9402204 | On the embedding of 2-concave Orlicz spaces into $L^1$ | In [K--S 1] it was shown that
$$ \underset {\pi} \to {\text{Ave}} (\sum_{i=1}^{n}|x_i a_{\pi(i)}|^2)^{\frac
{1}{2}} $$
is equivalent to an Orlicz norm whose Orlicz function is 2-concave. Here we
give a formula for the sequence $a_1, a_2,....,a_n$ so that the above
expression is equivalent to a given Orlicz norm. | 1994-02-01 | 2016-09-06 | [
"math.FA"
] | Carsten Sch\"utt |
math/9402203 | A Dvoretsky Theorem for Polynomials | We lift upper and lower estimates from linear functionals to $n$-homogeneous
polynomials and using this result show that $l_\infty$ is finitely represented
in the space of $n$-homogeneous polynomials, $n\ge2$, for any infinite
dimensional Banach space. Refinements are also given. | 1994-02-01 | 2009-09-25 | [
"math.FA"
] | Sean Dineen |
math/9401207 | On a weak type (1,1) inequality for a maximal conjugate function | In a celebrated paper, Burkholder, Gundy, and Silverstein used Brownian
motion to derive a maximal function characterization of H^p spaces for 0 < p <
infinity. In this paper, we show that their method extends to higher dimensions
and yields a dimension-free weak type (1,1) estimate for a conjugate function
on the N-di... | 1994-01-18 | 2008-02-03 | [
"math.FA"
] | N. Asmar, Stephen J. Montgomery-Smith |
math/9401206 | Q-Reflexive Banach spaces | Let $E$ be a Banach space and, for any positive integer $n$, let ${\cal
P}(^nE)$ denote the Banach space of continuous $n$-homogeneous polynomials on
$E$. Davie and Gamelin showed that the natural extension mapping from ${\cal
P}(^nE)$ to ${\cal P}(^nE^{\ast\ast})$ is an isometry into the latter space.
Here, we investi... | 1994-01-05 | 2016-09-06 | [
"math.FA"
] | Richard M. Aron, Sean Dineen |
math/9401205 | Type and cotype with respect to arbitrary orthonormal systems | Let $\on_{k \in \nz}$ be an orthonormal system on some $\sigma$-finite
measure space $(\Om,p)$. We study the notion of cotype with respect to $\Phi$
for an operator $T$ between two Banach spaces $X$ and $Y$, defined by $\fco T
:= \inf$ $c$ such that \[ \Tfmm \pl \le \pl c \pll \gmm \hspace{.7cm}\mbox{for
all}\hspace{.7... | 1994-01-04 | 2016-09-06 | [
"math.FA"
] | Stefan Geiss, Marius Junge |
math/9401221 | Pointwise convergence of wavelet expansions | In this note we announce that under general hypotheses, wavelet-type
expansions (of functions in $L^p,\ 1\leq p \leq \infty$, in one or more
dimensions) converge pointwise almost everywhere, and identify the Lebesgue set
of a function as a set of full measure on which they converge. It is shown that
unlike the Fourier ... | 1994-01-01 | 2016-09-06 | [
"math.FA"
] | Susan E. Kelly, Mark A. Kon, Louise A. Raphael |
math/9412204 | The normalized cyclomatic quotient associated with presentations of
finitely generated groups | Given the Cayley graph of a finitely generated group $G$, with respect to a
presentation $G^{\alpha}$ with $n$ generators, the quotient of the rank of the
fundamental group of subgraphs of the Cayley graph by the cardinality of the
set of vertices of the subgraphs gives rise to the definition of the normalized
cyclomat... | 1994-12-28 | 2008-02-03 | [
"math.GR"
] | Amnon Rosenmann |
math/9412203 | When Schrier transversals grow wild | Schreier formula for the rank of a subgroup of finite index of a finitely
generated free group $F$ is generalized to an arbitrary (even infinitely
generated) subgroup $H$ through the Schreier transversals of $H$ in $F$. The
rank formula may also be expressed in terms of the cogrowth of $H$. We
introduce the rank-growth... | 1994-12-28 | 2008-02-03 | [
"math.GR"
] | Amnon Rosenmann |
math/9411203 | Regular Cocycles and Biautomatic Structures | Let $E$ be a virtually central extension of the group $G$ by a finitely
generated abelian group $A$. We show that $E$ carries a biautomatic structure
if and only if $G$ has a biautomatic structure $L$ for which the cohomology
class of the extension is represented by an $L$-regular cocycle. Moreover, a
cohomology class ... | 1994-11-07 | 2016-09-06 | [
"math.GR"
] | Walter D. Neumann and Lawrence Reeves |
math/9410220 | The flag-transitive tilde and Petersen-type geometries are all known | We announce the classification of two related classes of flag-transitive
geometries. There is an infinite family of such geometries, related to the
nonsplit extensions $3^{[{n\atop 2}]_{_2}}\cdot \SP_{2n}(2)$, and twelve
sporadic examples coming from the simple groups $M_{22}$, $M_{23}$, $M_{24}$,
$He$, $Co_1$, $Co_2$,... | 1994-10-01 | 2009-09-25 | [
"math.GR"
] | Alexander A. Ivanov, Sergey V. Shpectorov |
math/9406206 | A new problem in string searching | We describe a substring search problem that arises in group presentation
simplification processes. We suggest a two-level searching model: skip and
match levels. We give two timestamp algorithms which skip searching parts of
the text where there are no matches at all and prove their correctness. At the
match level, we ... | 1994-06-15 | 2009-09-25 | [
"math.GR"
] | George Havas and Jin Xian Lian |
math/9406204 | Applications of substring searching to group presentations | An important way for describing groups is by finite presentations. Large
presentations arise in practice which are poorly suited for either human or
computer use. Presentation simplification processes which take bad
presentations and produce good presentations have been developed. Substantial
use is made of substring s... | 1994-06-15 | 2009-09-25 | [
"math.GR"
] | George Havas and Mark Ollila |
math/9406207 | Applications of computational tools for finitely presented groups | Computer based techniques for recognizing finitely presented groups are quite
powerful. Tools available for this purpose are outlined. They are available
both in stand-alone programs and in more comprehensive systems. A general
computational approach for investigating finitely presented groups by way of
quotients and s... | 1994-06-15 | 2008-02-03 | [
"math.GR"
] | George Havas and Edmund F. Robertson |
math/9406203 | Algorithms for groups | Group theory is a particularly fertile field for the design of practical
algorithms. Algorithms have been developed across the various branches of the
subject and they find wide application. Because of its relative maturity,
computational group theory may be used to gain insight into the general
structure of algebraic ... | 1994-06-15 | 2009-09-25 | [
"math.GR"
] | John Cannon and George Havas |
math/9406202 | Coset enumeration strategies | A primary reference on computer implementation of coset enumeration
procedures is a 1973 paper of Cannon, Dimino, Havas and Watson. Programs and
techniques described there are updated in this paper. Improved coset definition
strategies, space saving techniques and advice for obtaining improved
performance are included.... | 1994-06-15 | 2008-02-03 | [
"math.GR"
] | George Havas |
math/9406205 | Recognizing badly presented Z-modules | Finitely generated Z-modules have canonical decompositions. When such modules
are given in a finitely presented form there is a classical algorithm for
computing a canonical decomposition. This is the algorithm for computing the
Smith normal form of an integer matrix. We discuss algorithms for Smith normal
form computa... | 1994-06-15 | 2009-09-25 | [
"math.GR"
] | George Havas, Derek F. Holt and Sarah Rees |
math/9404203 | Central quotients of biautomatic groups | The quotient of a biautomatic group by a subgroup of the center is shown to
be biautomatic. The main tool used is the Neumann-Shapiro triangulation of
$S^{n-1}$, associated to a biautomatic structure on ${\Bbb Z}^n$. As an
application, direct factors of biautomatic groups are shown to be biautomatic. | 1994-04-26 | 2008-02-03 | [
"math.GR"
] | Lee Mosher |
math/9404202 | Hyperbolic buildings, affine buildings and automatic groups | We see that a building whose Coxeter group is hyperbolic is itself
hyperbolic. Thus any finitely generated group acting co-compactly on such a
building is hyperbolic, hence automatic. We turn our attention to affine
buildings and consider a group $\Gamma$ which acts simply transitively and in a
``type-rotating'' way on... | 1994-04-22 | 2009-09-25 | [
"math.GR"
] | Donald I. Cartwright and Michael Shapiro |
math/9401201 | Automatic structures, rational growth and geometrically finite
hyperbolic groups | We show that the set $SA(G)$ of equivalence classes of synchronously
automatic structures on a geometrically finite hyperbolic group $G$ is dense in
the product of the sets $SA(P)$ over all maximal parabolic subgroups $P$. The
set $BSA(G)$ of equivalence classes of biautomatic structures on $G$ is
isomorphic to the pro... | 1994-01-05 | 2009-10-28 | [
"math.GR"
] | Walter D. Neumann and Michael Shapiro |
math/9411204 | The structure of branching in Anosov flows of 3-manifolds | In this article we study the topological structure of the lifts to the
universal of the stable and unstable foliations of $3$-dimensional Anosov
flows. In particular we consider the case when these foliations do not have
Hausdorff leaf space. We completely determine the structure of the set of non
separated leaves from... | 1994-11-28 | 2009-09-25 | [
"math.GT",
"math.DS"
] | Sergio R. Fenley |
math/9411211 | The Structure and Enumeration of Link Projections | We define a decomposition of link projections whose pieces we call atoroidal
graphs. We describe a surgery operation on these graphs and show that all
atoroidal graphs can be generated by performing surgery repeatedly on a family
of well known link projections. This gives a method of enumerating atoroidal
graphs and he... | 1994-11-07 | 2009-09-25 | [
"math.GT"
] | Martin Bridgeman |
math/9410218 | On the geometric and topological rigidity of hyperbolic 3-manifolds | A homotopy equivalence between a hyperbolic 3-manifold and a closed
irreducible 3-manifold is homotopic to a homeomorphsim provided the hyperbolic
manifold satisfies a purely geometric condition. There are no known examples of
hyperbolic 3-manifolds which do not satisfy this condition. | 1994-10-01 | 2016-09-06 | [
"math.GT"
] | David Gabai |
math/9410215 | Exceptional surgery on knots | Let $M$ be an irreducible, compact, connected, orientable 3-manifold whose
boundary is a torus. We show that if $M$ is hyperbolic, then it admits at most
six finite/cyclic fillings of maximal distance 5. Further, the distance of a
finite/cyclic filling to a cyclic filling is at most 2. If $M$ has a
non-boundary-paralle... | 1994-10-01 | 2016-09-06 | [
"math.GT"
] | Steven Boyer, Xingru Zhang |
math/9409232 | Quasi-projections in Teichm\"uller space | We consider a geometric property of the closest-points projection to a
geodesic in Teichm\"uller space: the projection is called contracting if
arbitrarily large balls away from the geodesic project to sets of bounded
diameter. (This property always holds in negatively curved spaces.) It is shown
here to hold if and on... | 1994-09-30 | 2016-09-06 | [
"math.GT",
"math.DS"
] | Yair Minsky |
math/9409209 | A User's Guide to the Mapping Class Group: Once Punctured Surfaces | This document is a practical guide to computations using an automatic
structure for the mapping class group of a once-punctured, oriented surface
$S$. We describe a quadratic time algorithm for the word problem in this group,
which can be implemented efficiently with pencil and paper. The input of the
algorithm is a wo... | 1994-09-09 | 2016-09-06 | [
"math.GT"
] | Lee Mosher |
math/9407222 | Extremal length estimates and product regions in Teichm\"uller space | We study the Teichm\"uller metric on the Teichm\"uller space of a surface of
finite type, in regions where the injectivity radius of the surface is small.
The main result is that in such regions the Teichm\"uller metric is
approximated up to bounded additive distortion by the sup metric on a product
of lower dimensiona... | 1994-07-05 | 2016-09-06 | [
"math.GT"
] | Yair Minsky |
math/9407221 | Diffeomorphisms of manifolds with finite fundamental group | We show that the group ${\Cal D}(M)$ of pseudoisotopy classes of
diffeomorphisms of a manifold of dimension $\geq 5$ and of finite fundamental
group is commensurable to an arithmetic group. As a result $\pi_0(\text{{\it
Diff\,M}})$ is a group of finite type. | 1994-07-01 | 2009-09-25 | [
"math.GT",
"math.AT"
] | Georgia Triantafillou |
math/9407217 | Alexander's and Markov's theorems in dimension four | Alexander's and Markov's theorems state that any link type in $R^3$ is
represented by a closed braid and that such representations are related by some
elementary operations called Markov moves. We generalize the notion of a braid
to that in 4-dimensional space and establish an analogue of these theorems. | 1994-07-01 | 2016-09-06 | [
"math.GT"
] | Seiichi Kamada |
math/9404232 | Recurrence relations and asymptotics for four-manifold invariants | The polynomial invariants $q_d$ for a large class of smooth 4-manifolds are
shown to satisfy universal relations. The relations reflect the possible genera
of embedded surfaces in the 4-manifold and lead to a structure theorem for the
polynomials. As an application, one can read off a lower bound for the genera
of embe... | 1994-04-01 | 2016-09-06 | [
"math.GT",
"math.DG"
] | Peter B. Kronheimer, Tomasz S. Mrowka |
math/9404228 | Characterizing algebras of smooth functions on manifolds | Among all $C^\infty$-algebras we characterize those which are algebras of
smooth functions on smooth separable Hausdorff manifolds. | 1994-04-01 | 2008-02-03 | [
"math.GT",
"math.DG"
] | Peter W. Michor, Ji\v{r}i Van\v{z}ura |
math/9404229 | Responses to ``Theoretical Mathematics: Toward a cultural synthesis of
mathematics and theoretical physics'', by A. Jaffe and F. Quinn | This article is a collection of letters solicited by the editors of the
Bulletin in response to a previous article by Jaffe and Quinn
[math.HO/9307227]. The authors discuss the role of rigor in mathematics and the
relation between mathematics and theoretical physics. | 1994-04-01 | 2010-04-07 | [
"math.HO"
] | Michael Atiyah, Armand Borel, G. J. Chaitin, Daniel Friedan, James
Glimm, Jeremy J. Gray, Morris W. Hirsch, Saunder MacLane, Benoit B.
Mandelbrot, David Ruelle, Albert Schwarz, Karen Uhlenbeck, Ren\'e Thom,
Edward Witten, Christopher Zeeman |
math/9404236 | On proof and progress in mathematics | In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms
of progress in mathematics that are not captured by formal proofs of theorems,
especially in his own work in the theory of foliations and geometrization of
3-manifolds and dynamical systems. | 1994-04-01 | 2008-02-03 | [
"math.HO"
] | William P. Thurston |
math/9404233 | Editor's column (on an article by Jaffe and Quinn) | This note is a preface to various responses [math.HO/9404229,math.HO/9404236]
to an opinion piece by Jaffe and Quinn [math.HO/9307227] on the relationship
between mathematics and theoretical physics. | 1994-04-01 | 2016-09-06 | [
"math.HO"
] | Richard S. Palais |
math/9404231 | Response to comments on ``Theoretical mathematics'' | The authors discuss various objections and rejoinders in the collected
responses [math.HO/9404229,math.HO/9404236] to their original article on the
relationship between mathematics and theoretical physics [math.HO/9307227]. | 1994-04-01 | 2009-09-25 | [
"math.HO"
] | Arthur Jaffe, Frank Quinn |
math/9409211 | A Comparison of Continuously Controlled and Controlled K-theory | We define an unreduced version of the e-controlled lower $K$-theoretic groups
of Ranicki and Yamasaki, and Quinn. We show that the reduced versions of our
groups coincide (in the inverse limit and its first derived, $\lim^1$) with
those of Ranicki and Yamasaki. We also relate the controlled groups to the
continuously c... | 1994-09-16 | 2016-09-06 | [
"math.KT"
] | Douglas R. Anderson, Francis X. Connolly, Hans J. Munkholm |
math/9412231 | Uniformization and Skolem functions in the class of trees | The monadic second-order theory of trees allows quantification over elements
and over arbitrary subsets. We classify the class of trees with respect to the
question: does a tree T have definable Skolem functions (by a monadic formula
with parameters)? This continues [LiSh539] where the question was asked only
with resp... | 1994-12-15 | 2008-02-03 | [
"math.LO"
] | Shmuel Lifsches, Saharon Shelah |
math/9412229 | The universality spectrum: Consistency for more classes | We deal with consistency results for the existence of universal models in
natural classes of models (more exactly--a somewhat weaker version). We apply a
result on quite general family to T_feq and to the class of triangle-free
graphs. | 1994-12-15 | 2016-09-06 | [
"math.LO"
] | Saharon Shelah |
math/9412230 | The cofinality spectrum of the infinite symmetric group | A group G that is not finitely generated can be written as the union of a
chain of proper subgroups. The cofinality spectrum of G, written CF(S), is the
set of regular cardinals lambda such that G can be expressed as the union of a
chain of lambda proper subgroups. The cofinality of G, written c(G), is the
least elemen... | 1994-12-15 | 2016-09-06 | [
"math.LO",
"math.GR"
] | Saharon Shelah, Simon Thomas |
math/9412209 | Some results on nonstationry ideal 2 | This is a continuation of "Some results on nonstationry ideal". The upper
bound on precipitousness of NS_lambda^+ for a regular lambda given in this
paper is proved to be exact.It is shown that saturatedness of NS_kappa^aleph_0
over inaccessible kappa requires at least o(kappa)=kappa^++.The upper bounds on
the strength... | 1994-12-06 | 2008-02-03 | [
"math.LO"
] | Moti Gitik |
math/9412208 | Possible pcf algebras | There exists a family $\{B_{\alpha}\}_{\alpha<\omega_1}$ of sets of countable
ordinals such that
o $\max B_{\alpha}=\alpha$,
o if $\alpha\in B_{\beta}$ then $B_{\alpha}\subseteq B_{\beta}$,
o if $\lambda\leq \alpha$ and $\lambda$ is a limit ordinal then
$B_{\alpha}\cap\lambda$ is not in the ideal generated by the... | 1994-12-03 | 2016-09-06 | [
"math.LO"
] | Thomas Jech and Saharon Shelah |
math/9411208 | Semi-Cohen Versus Cohen Algebras | We show that there are semi-Cohen Boolean algebras which cannot be completely
embedded into Cohen Boolean algebras. Using the ideas from this proof, we give
a simpler argument for a theorem of S. Koppelberg and S. Shelah, stating that
there are complete subalgebras of Cohen algebras which are not Cohen
themselves. | 1994-11-22 | 2008-02-03 | [
"math.LO"
] | Jind\v{r}ich Zapletal |
math/9411207 | Large ordinals | Let $j$ be an elementary embedding of $V_{\lambda}$ into $V_{\lambda}$ that
is not the identity, and let $\kappa$ be the critical point of $j$. Let $\Cal
A$ be the closure of $\{j\}$ under the operation $a (b)$ of application, and
let $\Omega$ be the closure of $\{\kappa\}$ under the operation $\min \{\xi:
a(\xi) \ge b... | 1994-11-19 | 2008-02-03 | [
"math.LO"
] | Thomas Jech |
math/9411236 | On finite rigid structures | The main result of this paper is a probabilistic construction of finite rigid
structures. It yields a finitely axiomatizable class of finite rigid structures
where no L^omega_{infty, omega} formula with counting quantifiers defines a
linear order. | 1994-11-15 | 2016-09-06 | [
"math.LO",
"cs.LO"
] | Yuri Gurevich, Saharon Shelah |
math/9411234 | The essentially free spectrum of a variety | We partially prove a conjecture from [MkSh:366] which says that the spectrum
of almost free, essentially free, non-free algebras in a variety is either
empty or consists of the class of all successor cardinals. | 1994-11-15 | 2008-02-03 | [
"math.LO",
"math.RA"
] | Alan H. Mekler, Saharon Shelah, Otmar Spinas |
math/9411235 | McColm conjecture | Gregory McColm conjectured that positive elementary inductions are bounded in
a class K of finite structures if every (FO + LFP) formula is equivalent to a
first-order formula in K. Here (FO + LFP) is the extension of first-order logic
with the least fixed point operator. We disprove the conjecture. Our main
results ar... | 1994-11-15 | 2016-09-06 | [
"math.LO",
"cs.LO"
] | Yuri Gurevich, Neil Immerman, Saharon Shelah |
math/9411206 | Measurability of functions with approximately continuous vertical
sections and measurable horizontal sections | A function f:R -> R is approximately continuous iff it is continuous in the
density topology, i.e., for any ordinary open set U the set E=f^{-1}(U) is
measurable and has Lebesgue density one at each of its points. Denjoy proved
that approximately continuous functions are Baire 1., i.e., pointwise For any
f:R^2 -> R def... | 1994-11-07 | 2016-09-06 | [
"math.LO"
] | M. Laczkovich and Arnold W. Miller |
math/9411205 | Souslin's Hypothesis and Convergence in Category | A sequence of functions f_n: X -> R from a Baire space X to the reals is said
to converge in category iff every subsequence has a subsequence which converges
on all but a meager set. We show that if there exists a Souslin Tree then there
exists a nonatomic Baire space X such that every sequence which converge in
catego... | 1994-11-01 | 2008-02-03 | [
"math.LO"
] | Arnold W. Miller |
math/9410201 | Cardinal invariants concerning functions whose sum is almost continuous | A function f from reals to reals (f:R->R) is almost continuous (in the sense
of Stallings) iff every open set in the plane which contains the graph of f
contains the graph of a continuous function.
Natkaniec showed that for any family F of continuum many real functions there
exists g:R->R such that f+g is almost cont... | 1994-10-26 | 2016-09-06 | [
"math.LO"
] | Krzysztof Ciesielski and Arnold W. Miller |
math/9410206 | Graph-Based Logic and Sketches 1: The General Framework | Traditional treatments of formal logic provide: 1. A syntax for formulas. 2.
An inference relation between sets of formulas. 3. A rule for assigning meaning
to formulas (semantics) that is sound with respect to the inference relation.
First order logic, the logic and semantics of programming languages, and the
langua... | 1994-10-17 | 2016-09-06 | [
"math.LO"
] | Atish Bagchi, Charles Wells |
math/9409207 | Universal abelian groups | We examine the existence of universal elements in classes of infinite abelian
groups. The main method is using group invariants which are defined relative to
club guessing sequences. We prove, for example:
Theorem: For $n\ge 2$, there is a purely universal separable $p$-group in
$\aleph_n$ if, and only if, $\cont\le ... | 1994-09-17 | 2016-09-06 | [
"math.LO"
] | Menachem Kojman and Saharon Shelah |
math/9409204 | Infinite homogeneous bipartite graphs with unequal sides | We call a bipartite graph {\it homogeneous} if every finite partial
automorphism which respects left and right can be extended to a total
automorphism.
A $(\kappa,{\lambda} )$ bipartite graph is a bipartite graph with left side
of size $\kappa$ and right side of size ${\lambda}$. We show, using a theorem
of Hrushovsk... | 1994-09-06 | 2009-09-25 | [
"math.LO"
] | Martin Goldstern, R. Grossberg, Menachem Kojman |
math/9409206 | Universal bridge-free graphs | We prove that there is no countable universal $B_n$-free graph for all $n$
and that there is no countable universal graph in the class of graphs omitting
all cycles of length at most $2k$ for $k\ge 2$. | 1994-09-06 | 2008-02-03 | [
"math.LO"
] | Martin Goldstern and Menachem Kojman |
math/9409205 | Homogeneous families and their automorphism groups | A homogeneous family of subsets over a given set is one with a very ``rich''
automorphism group. We prove the existence of a bi-universal element in the
class of homogeneous families over a given infinite set and give an explicit
construction of $2^\cont$ isomorphism types of homogeneous families over a
countable set. | 1994-09-06 | 2009-09-25 | [
"math.LO"
] | Menachem Kojman and Saharon Shelah |
math/9409203 | Small forcings and Cohen reals | We prove it consistent relative to ZFC that all nontrivial forcings of size
$\aleph _1$ add a Cohen real. | 1994-09-02 | 2009-09-25 | [
"math.LO"
] | Jind\v{r}ich Zapletal |
math/9409201 | OTTER Experiments in a System of Combinatory Logic | This paper describes some experiments involving the automated theorem-proving
program OTTER in the system TRC of illative combinatory logic. We show how
OTTER can be steered to find a contradiction in an inconsistent variant of TRC,
and present some experimentally discovered identities in TRC. | 1994-09-02 | 2008-02-03 | [
"math.LO"
] | Thomas Jech |
math/9409202 | Projective Stationary Sets and Strong Reflection Principle | We study projective stationary sets. The Projective Stationary Reflection
principle is the statement that every projective stationary set contains an
increasing continuous $\in$--chain of length $\omega_1$. We show that if
Martin's Maximum holds, then the Projective Stationary Reflection Principle
holds. Also it is equ... | 1994-09-02 | 2009-09-25 | [
"math.LO"
] | Qi Feng and Thomas Jech |
math/9408204 | On the logical strength of Nash-Williams' theorem on transfinite
sequences | We show that Nash-Williams' theorem asserting that the countable transfinite
sequences of elements of a better-quasi-ordering ordered by embeddability form
a better-quasi-ordering is provable in the subsystem of second order arithmetic
Pi^1_1-CA_0 but is not equivalent to Pi^1_1-CA_0. We obtain some partial
results tow... | 1994-08-30 | 2009-09-25 | [
"math.LO"
] | Alberto Marcone |
math/9408214 | Martin's Axiom and Delta^2_1 well-ordering of the reals | Assuming an inaccessible cardinal kappa, there is a generic extension in
which MA + 2^{aleph_0} = kappa holds and the reals have a Delta^2_1
well-ordering. | 1994-08-15 | 2008-02-03 | [
"math.LO"
] | Uri Abraham, Saharon Shelah |
math/9408215 | More forcing notions imply diamond | We prove that the Sacks forcing collapses the continuum onto the dominating
number d, answering the question of Carlson and Laver. Next we prove that if a
proper forcing of the size at most continuum collapses omega_2 then it forces
diamond_{omega_1} . | 1994-08-15 | 2009-09-25 | [
"math.LO"
] | Andrzej Ros{\l}anowski, Saharon Shelah |
math/9408213 | Almost free algebras | The essentially non-free spectrum is the class of uncountable cardinals kappa
in which there is an essentially non-free algebra of cardinality kappa which is
almost free. In L, the essentially non-free spectrum of a variety is entirely
determined by whether or not the construction principle holds. In ZFC may be
more co... | 1994-08-15 | 2016-09-06 | [
"math.LO",
"math.RA"
] | Alan H. Mekler, Saharon Shelah |
math/9408203 | Co-elementary equivalence, co-elementary maps, and generalized arcs | By a {\bf generalized arc\/} we mean a continuum with exactly two
non-separating points; an {\bf arc} is a metrizable generalized arc. It is well
known that any two arcs are homeomorphic (to the real closed unit interval); we
show that any two generalized arcs are co-elementarily equivalent, and that
co-elementary imag... | 1994-08-10 | 2009-09-25 | [
"math.LO"
] | Paul Bankston |
math/9408201 | Properties of the Class of Measure Separable Compact Spaces | We investigate properties of the class of compact spaces on which every
regular Borel measure is separable. This class will be referred to as MS.
We discuss some closure properties of MS, and show that some simply defined
compact spaces, such as compact ordered spaces or compact scattered spaces, are
in MS. Most of t... | 1994-08-09 | 2009-09-25 | [
"math.LO"
] | Mirna D\v{z}amonja and Kenneth Kunen |
math/9408202 | Remarks on aleph_1-metrizable not metrizable first countable spaces and
CWH | CWH, CWN stand for collectionwise Hausdorff and collectionwise normal
respectively. We analyze the statement "there is a lambda-CWH not CWH first
countable (Hausdorff topological) space". We prove the existence of such a
space under various conditions, show its equivalence to: there is a lambda-CWN
not CWN first counta... | 1994-08-09 | 2016-09-06 | [
"math.LO"
] | Saharon Shelah |
math/9407205 | Mutually Generics and Perfect Free Subsets | We discuss ways of adjoining perfect sets of mutually generic random reals.
In particular, we show that if V \sub W are models of ZFC and W contains a
dominating real over V, then W[r], where r is random over W, contains a perfect
tree of mutually random reals over V. This result improves an earlier result by
Bartoszyn... | 1994-07-17 | 2016-09-06 | [
"math.LO"
] | J\"org Brendle |
math/9407207 | Evasion and prediction II | A subgroup G \leq Z^omega exhibits the Specker phenomenon if every
homomorphism G \to Z maps almost all unit vectors to 0. We give several
combinatorial characterizations of the cardinal se, the size of the smallest G
\leq Z^omega exhibiting the Specker phenomenon.
We also prove the consistency of b < e, where b is t... | 1994-07-17 | 2016-09-06 | [
"math.LO"
] | J\"org Brendle and Saharon Shelah |
math/9407208 | Nicely generated and chaotic ideals | We show that if the real line is the disjoint union of kappa meager sets such
that every meager set is contained in a countable union of them, then kappa =
omega_1. This answers a question addressed by J. Cichon. We also prove two
theorems saying roughly that any attempt to produce the isomorphism type of the
meager id... | 1994-07-17 | 2008-02-03 | [
"math.LO"
] | J\"org Brendle |
math/9407204 | Strolling through Paradise | With each of the usual tree forcings I (e.g., I = Sacks forcing S, Laver
forcing L, Miller forcing M, Mathias forcing R, etc.) we associate a
sigma--ideal i^0 on the reals as follows: A \in i^0 iff for all T \in I there
is S \leq T (i.e. S is stronger than T or, equivalently, S is a subtree of T)
such that A \cap [S] =... | 1994-07-17 | 2016-09-06 | [
"math.LO"
] | J\"org Brendle |
math/9407206 | Forcing tightness in products of fans | The theta--fan F_theta is the quotient space obtained by identifying the
non--isolated points of the product theta \times (omega+1) with a single point
\infty. (Here, theta has the discrete topology and omega+1 has the order
topology.)
We define several notions of forcing that allow us to manipulate the
tightness t o... | 1994-07-17 | 2016-09-06 | [
"math.LO"
] | J\"org Brendle and Tim LaBerge |
math/9407203 | Reductions Between Cardinal Characteristics of the Continuum | We discuss two general aspects of the theory of cardinal characteristics of
the continuum, especially of proofs of inequalities between such
characteristics. The first aspect is to express the essential content of these
proofs in a way that makes sense even in models where the inequalities hold
trivially (e.g., because... | 1994-07-12 | 2008-02-03 | [
"math.LO"
] | Andreas Blass |
math/9406219 | Large normal ideals concentrating on a fixed small cardinality | A property of a filter, a kind of large cardinal property, suffices for the
proof in Liu Shelah [LiSh:484] and is proved consistent as required there. A
natural property which looks better, not only is not obtained here, but is
shown to be false. On earlier related theorems see Gitik Shelah [GiSh310]. | 1994-06-15 | 2008-02-03 | [
"math.LO"
] | Saharon Shelah |
math/9406229 | Adding one random real | We study the cardinal invariants of measure and category after adding one
random real. In particular, we show that the number of measure zero subsets of
the plane which are necessary to cover graphs of all continuous functions maybe
large while the covering for measure is small. | 1994-06-15 | 2016-09-06 | [
"math.LO"
] | Tomek Bartoszy\'nski, Andrzej Ros{\l}anowski, Saharon Shelah |
math/9406228 | Every null additive set of reals is meager additive | We show that every null-additive set is meager-additive, where:
(1) a set X subseteq 2^omega is null-additive if for every Lebesgue null set
A subseteq 2^omega, X+A is null too;
(2) we say that X subseteq 2^omega is meager-additive if for every A subseteq
2^omega which is meager also X+A is meager. | 1994-06-15 | 2016-09-06 | [
"math.LO"
] | Saharon Shelah |
math/9405208 | Kolmogorov complexity and instance complexity of recursively enumerable
sets | We study in which way Kolmogorov complexity and instance complexity affect
properties of r.e. sets. We show that the well-known 2log n upper bound on the
Kolmogorov complexity of initial segments of r.e.\ sets is optimal and
characterize the T-degrees of r.e. sets which attain this bound. The main part
of the paper is ... | 1994-05-25 | 2009-09-25 | [
"math.LO"
] | Martin Kummer |
math/9405207 | Bqo is Pi^1_2-complete | In this paper we prove that the set of countable bqos (viewed as a subset of
the Cantor space) is Pi^1_2-complete. The notion of bqo or better
quasi-ordering arises from combinatorics and is a generalization of the
canonical example of a Pi^1_1-complete notion, i.e. that of countable
well-ordering. The Pi^1_2-completen... | 1994-05-24 | 2010-03-26 | [
"math.LO"
] | Alberto Marcone |
math/9405206 | Subgroups of the Baer-Specker Group with Few Endomorphisms but Large
Dual | The Baer-Specker group is the product of countably many copies of the
additive group Z of integers. Assuming the continuum hypothesis, we construct a
pure subgroup G of the Baer-Specker group with the following properties. Every
endomorphism of G differs from a scalar multiplication by an endomorphism of
finite rank. Y... | 1994-05-23 | 2016-09-06 | [
"math.LO"
] | Andreas Blass and R\"udiger G\"obel |
math/9405202 | Simple Cardinal Characteristics of the Continuum | We classify many cardinal characteristics of the continuum according to the
complexity, in the sense of descriptive set theory, of their definitions. The
simplest characteristics (boldface Sigma^0_2 and, under suitable restrictions,
Pi^0_2) are shown to have pleasant properties, related to Baire category. We
construct ... | 1994-05-20 | 2009-09-25 | [
"math.LO"
] | Andreas Blass |
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