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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