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math/9309210
Bounds on the tail probability of U-statistics and quadratic forms
The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear $k$-correlations of $n>k$ independent random variables.
1993-09-13
2016-09-06
[ "math.FA", "math.PR" ]
Victor H. de la Pe\~na, Stephen J. Montgomery-Smith
math/9309211
Decoupling Inequalities for the Tail Probabilities of Multivariate U-statistics
In this paper the following result, which allows one to decouple U-Statistics in tail probability, is proved in full generality. Theorem 1. Let $X_i$ be a sequence of independent random variables taking values in a measure space $S$, and let $f_{i_1...i_k}$ be measurable functions from $S^k$ to a Banach space $B$. Le...
1993-09-13
2008-02-03
[ "math.FA" ]
Victor H. de la Pe\~na, Stephen J. Montgomery-Smith
math/9308207
Regular operators between non-commutative $L_p$-spaces
We introduce the notion of a regular mapping on a non-commutative $L_p$-space associated to a hyperfinite von Neumann algebra for $1\le p\le \infty$. This is a non-commutative generalization of the notion of regular or order bounded map on a Banach lattice. This extension is based on our recent paper [P3], where we int...
1993-08-24
2016-09-06
[ "math.FA" ]
Gilles Pisier
math/9308208
Bilinear forms on exact operator spaces and B(H)\otimes B(H)
Let $E,F$ be exact operators (For example subspaces of the $C^*$-algebra $K(H)$ of all the compact operators on an infinite dimensional Hilbert space $H$). We study a class of bounded linear maps $u\colon E\to F^*$ which we call tracially bounded. In particular, we prove that every completely bounded (in short $c.b.$) ...
1993-08-24
2016-09-06
[ "math.FA" ]
Marius Junge, Gilles Pisier
math/9308206
The $M$-ideal structure of some algebras of bounded linear operators
Let $1<p,\,q<\infty$. It is shown for complex scalars that there are no nontrivial $M$-ideals in $L(L_p[0,1])$ if $p\neq 2$, and $K(\ell_p(\ell_q^n)$ is the only nontrivial $M$-ideal in $L(\ell_p(\ell_q^n)$. This proves a conjecture of C.-M. Cho and W. B. Johnson.
1993-08-13
2008-02-03
[ "math.FA" ]
Nigel J. Kalton, Dirk Werner
math/9308205
On impossible extensions of Krivine's Theorem
We give examples of two Banach spaces. One Banach space has no spreading model which contains $\ell_p$ ($1\le p<\infty$) or $c_0$. The other space has an unconditional basis for which $\ell_p$ ($1\le p<\infty$) and $c_0$ are block finitely represented in all block bases.
1993-08-10
2016-09-06
[ "math.FA" ]
Edward Odell, Thomas Schlumprecht
math/9308204
Exact operator spaces
In this paper, we study {\it operator spaces\/} in the sense of the theory developed recently by Blecher-Paulsen [BP] and Effros-Ruan [ER1]. By an operator space, we mean a closed subspace $E\subset B(H)$, with $H$ Hilbert. We will be mainly concerned here with the ``geometry'' of {\it finite dimensional\/} operator ...
1993-08-09
2016-09-06
[ "math.FA" ]
Gilles Pisier
math/9307201
Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces
We present a spectral mapping theorem for continuous semigroups of operators on any Banach space $E$. The condition for the hyperbolicity of a semigroup on $E$ is given in terms of the generator of an evolutionary semigroup acting in the space of $E$-valued functions. The evolutionary semigroup generated by the propaga...
1993-07-08
2008-02-03
[ "math.FA" ]
Yuri D. Latushkin, Stephen J. Montgomery-Smith
math/9306210
Some stability properties of $c_0$-saturated spaces
A Banach space is $c_0$-saturated if all of its closed infinite dimensional subspaces contain an isomorph of $c_0$. In this article, we study the stability of this property under the formation of direct sums and tensor products. Some of the results are: (1) a slightly more general version of the fact that $c_0$-sums of...
1993-06-21
2016-09-06
[ "math.FA" ]
Denny H. Leung
math/9306212
A remark about distortion
In this note we show that every Banach space $X$ not containing $\ell_1^n$ uniformly and with unconditional basis contains an arbitrarily distortable subspace.
1993-06-21
2009-09-25
[ "math.FA" ]
Bernard Maurey
math/9306211
Banach spaces without local unconditional structure
For a large class of Banach spaces, a general construction of subspaces without local unconditional structure is presented. As an application it is shown that every Banach space of finite cotype contains either $l_2$ or a subspace without unconditional basis, which admits a Schauder basis. Some other interesting applic...
1993-06-21
2016-09-06
[ "math.FA" ]
R. Komowski, Nicole Tomczak-Jaegermann
math/9306209
The k_t--functional for the interpolation couple L^\infty(d\mu;L^1(d\nu)), L^\infty(d\nu;L^1(d\mu))
Let $(M,\mu)$ and $(N,\nu)$ be measure spaces. In this paper, we study the $K_t$--\,functional for the couple $$A_0=L^\infty(d\mu\,; L^1(d\nu))\,,~~A_1=L^\infty(d\nu\,; L^1(d\mu))\,. $$ Here, and in what follows the vector valued $L^p$--\,spaces $L^p(d\mu\,; L^q(d\nu))$ are meant in Bochner's sense. One of our main...
1993-06-09
2016-09-06
[ "math.FA" ]
Albrecht Hess, Gilles Pisier
math/9306208
Isometric stability property of certain Banach spaces
Let $E$ be one of the spaces $C(K)$ and $L_1$, $F$ be an arbitrary Banach space, $p>1,$ and $(X,\sigma)$ be a space with a finite measure. We prove that $E$ is isometric to a subspace of the Lebesgue-Bochner space $L_p(X;F)$ only if $E$ is isometric to a subspace of $F.$ Moreover, every isometry $T$ from $E$ into $L_p(...
1993-06-09
2016-09-06
[ "math.FA" ]
Alexander Koldobsky
math/9306207
Complex Interpolation and Regular Operators Between Banach
We study certain interpolation and extension properties of the space of regular operators between two Banach lattices. Let $R_p$ be the space of all the regular (or equivalently order bounded) operators on $L_p$ equipped with the regular norm. We prove the isometric identity $R_p = (R_\infty,R_1)^\theta$ if $\theta = 1...
1993-06-07
2016-09-06
[ "math.FA" ]
Gilles Pisier
math/9306206
Noncommutative vector valued $L_p$-spaces and completely $p$-summing maps
Let $E$ be an operator space in the sense of the theory recently developed by Blecher-Paulsen and Effros-Ruan. We introduce a notion of $E$-valued non commutative $L_p$-space for $1 \leq p < \infty$ and we prove that the resulting operator space satisfies the natural properties to be expected with respect to e.g. duali...
1993-06-07
2016-09-06
[ "math.FA" ]
Gilles Pisier
math/9305203
Random Banach spaces. The limitations of the method
We study the properties of "generic", in the sense of the Haar measure on the corresponding Grassmann manifold, subspaces of l^N_infinity of given dimension. We prove that every "well bounded" operator on such a subspace, say E, is a "small" perturbation of a multiple of identity, where "smallness" is defined intrinsic...
1993-05-11
2016-09-06
[ "math.FA" ]
P. Mankiewicz, Stanislaw J. Szarek
math/9304213
Prevalence: an addendum
The authors mention work of Christensen, Mycielski, Tsujii, and others which is closely related to a survey article by the first author [math.FA/9210220].
1993-04-01
2008-02-03
[ "math.FA", "math.DS" ]
Brian R. Hunt, Tim Sauer, James A. Yorke
math/9304206
Some isomorphically polyhedral Orlicz sequence spaces
A Banach space is polyhedral if the unit ball of each of its finite dimensional subspaces is a polyhedron. It is known that a polyhedral Banach space has a separable dual and is $c_0$-saturated, i.e., each closed infinite dimensional subspace contains an isomorph of $c_0$. In this paper, we show that the Orlicz sequenc...
1993-04-01
2016-09-06
[ "math.FA" ]
Denny H. Leung
math/9303203
W^*-derived sets of transfinite order of subspaces of dual Banach spaces
It is an English translation of the paper originally published in Russian and Ukrainian in 1987. In the appendix of his book S.Banach introduced the following definition Let $X$ be a Banach space and $\Gamma$ be a subspace of the dual space $X^*$. The set of all limits of $w^{*}$-convergent sequences in $\Gamma $ is ca...
1993-03-29
2010-09-07
[ "math.FA" ]
Mikhail I. Ostrovskii
math/9303206
Total subspaces with long chains of nowhere norming weak$^*$ sequential closures
If a separable Banach space $X$ is such that for some nonquasireflexive Banach space $Y$ there exists a surjective strictly singular operator $T:X\to Y$ then for every countable ordinal $\alpha $ the dual of $X$ contains a subspace whose weak$^*$ sequential closures of orders less than $\alpha $ are not norming over an...
1993-03-29
2010-09-07
[ "math.FA" ]
Mikhail I. Ostrovskii
math/9303205
A note on analytical representability of mappings inverse to integral operators
The condition onto pair ($F,G$) of function Banach spaces under which there exists a integral operator $T:F\to G$ with analytic kernel such that the inverse mapping $T^{-1}:$im$T\to F$ does not belong to arbitrary a priori given Borel (or Baire) class is found.
1993-03-29
2010-09-07
[ "math.FA" ]
Mikhail I. Ostrovskii
math/9303204
Total subspaces in dual Banach spaces which are not norming
The main result: the dual of separable Banach space $X$ contains a total subspace which is not norming over any infinite dimensional subspace of $X$ if and only if $X$ has a nonquasireflexive quotient space with the strictly singular quotient mapping.
1993-03-29
2010-09-07
[ "math.FA" ]
Mikhail I. Ostrovskii
math/9303202
Topologies on the set of all subspaces of a banach space and related questions of banach space geometry
For a Banach space $X$ we shall denote the set of all closed subspaces of $X$ by $G(X)$. In some kinds of problems it turned out to be useful to endow $G(X)$ with a topology. The main purpose of the present paper is to survey results on two the most common topologies on $G(X)$.
1993-03-29
2010-09-07
[ "math.FA" ]
Mikhail I. Ostrovskii
math/9303201
Spaces Of Lipschitz Functions On Banach Spaces
A remarkable theorem of R. C. James is the following: suppose that $X$ is a Banach space and $C \subseteq X$ is a norm bounded, closed and convex set such that every linear functional $x^* \in X^*$ attains its supremum on $C$; then $C$ is a weakly compact set. Actually, this result is significantly stronger than this s...
1993-03-04
2016-09-06
[ "math.FA" ]
Charles P. Stegall
math/9302216
Lyapunov theorems for Banach spaces
We present a spectral mapping theorem for semigroups on any Banach space $E$. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for $E$-valued functions. This characterization is given in terms of the spectrum of the generator of the semigroup of evolutionary oper...
1993-02-24
2016-09-06
[ "math.FA", "math.SP" ]
Yuri Latushkin, Stephen Montgomery-Smith
math/9302214
Bounded linear operators between C^*-algebras
Let $u:A\to B$ be a bounded linear operator between two $C^*$-algebras $A,B$. The following result was proved by the second author. Theorem 0.1. There is a numerical constant $K_1$ such that for all finite sequences $x_1,\ldots, x_n$ in $A$ we have $$\leqalignno{&\max\left\{\left\|\left(\sum u(x_i)^* u(x_i)\right)^{1...
1993-02-18
2016-09-06
[ "math.FA" ]
U. Haagerup, Gilles Pisier
math/9302215
Projections from a von~Neumann algebra onto a subalgebra
This paper is mainly devoted to the following question:\ Let $M,N$ be von~Neumann algebras with $M\subset N$, if there is a completely bounded projection $P\colon \ N\to M$, is there automatically a contractive projection $\widetilde P\colon \ N\to M$? We give an affirmative answer with the only restriction that $M$ ...
1993-02-18
2009-09-25
[ "math.FA" ]
Gilles Pisier
math/9302213
A factorization constant for $l^n_p
We prove that if PT is a factorization of the identity operator on \ell_p^n through \ell_{\infty}^k, then ||P|| ||T|| \geq Cn^{1/p-1/2}(log n)^{-1/2}. This is a corollary of a more general result on factoring the identity operator on a quasi-normed space through \ell_{\infty}^k.
1993-02-11
2016-09-06
[ "math.FA" ]
N. Tenney Peck
math/9302212
Dual Kadec-Klee norms and the relationships between Wijsman, slice and Mosco convergence
In this paper, we completely settle several of the open questions regarding the relationships between the three most fundamental forms of set convergence. In particular, it is shown that Wijsman and slice convergence coincide precisely when the weak star and norm topologies agree on the dual sphere. Consequently, a wea...
1993-02-09
2016-09-06
[ "math.FA" ]
Jonathan M. Borwein, J. Vanderwerff
math/9302211
Locally Lipschitz Functions and Bornological Derivatives
We study the relationships between Gateaux, weak Hadamard and Frechet differentiability and their bornologies for Lipschitz and for convex functions. In particular, Frechet and weak Hadamard differentiabily coincide for all Lipschitz functions if and only if the space is reflexive (an earlier paper of the first two aut...
1993-02-09
2016-09-06
[ "math.FA" ]
Jonathan M. Borwein, Marian Fabian, J. Vanderwerff
math/9302207
How many vectors are needed to compute (p,q)-summing norms?
We will show that for $q<p$ there exists an $\al < \infty$ such that \[ \pi_{pq}(T) \pl \le c_{pq} \pi_{pq}^{[n^{\alpha}]}(T) \mbox{for all $T$ of rank $n$.}\] Such a polynomial number is only possible if $q=2$ or $q<p$. Furthermore, the growth rate is linear if $q=2$ or $\frac{1}{q}-\frac{1}{p}>\frac{1}{2}$. Unless $\...
1993-02-04
2016-09-06
[ "math.FA" ]
M. Defant, Marius Junge
math/9302208
Every nonreflexive subspace of L_1[0,1] fails the fixed point property
The main result of this paper is that every non-reflexive subspace $Y$ of $L_1[0,1]$ fails the fixed point property for closed, bounded, convex subsets $C$ of $Y$ and nonexpansive (or contractive) mappings on $C$. Combined with a theorem of Maurey we get that for subspaces $Y$ of $L_1[0,1]$, $Y$ is reflexive if and onl...
1993-02-04
2016-09-06
[ "math.FA" ]
Paddy N. Dowling, Christopher J. Lennard
math/9302209
Lectures on maximal monotone operators
This is a 30 page set of lecture notes, in Plain TeX, which were prepared for and presented as a series of lectures (10 1/2 hours over two weeks) at the 2nd Summer School on Banach Spaces, Related Areas and Applications in Prague and Paseky, Czech Republic, during August, 1993. They consist of a largely self-contained ...
1993-02-04
2016-09-06
[ "math.FA" ]
Robert R. Phelps
math/9302206
Comparing gaussian and Rademacher cotype for operators on the space of continous functions
We will prove an abstract comparision principle which translates gaussian cotype in Rademacher cotype conditions and vice versa. More precisely, let $2\!<\!q\!<\!\infty$ and $T:\,C(K)\,\to\,F$ a linear, continous operator. T is of gaussian cotype q if and only if ( \summ_1^n (\frac{|| Tx_k||_F}{\sqrt{\log(k+1)}})^q...
1993-02-04
2016-09-06
[ "math.FA" ]
Marius Junge
math/9302205
Twisted sums and a problem of Klee
Let F be a quasi-linear map on a separable normed space X, and assume that F splits on an infinite-dimensional subspace of X. Then the twisted sum topology induced by F on the direct sum of X and the real line can be written as the supremum of a nearly convex topology and a trivial dual topology. (This partially answer...
1993-02-03
2008-02-03
[ "math.FA" ]
N. Tenney Peck
math/9302204
The Complete Continuity Property and Finite Dimensional Decompositions
A Banach space $\X$ has the complete continuity property (CCP) if each bounded linear operator from $L_1$ into $\X$ is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that a Banach space failing the CCP (resp., failing the CCP and failing cotype) has a...
1993-02-02
2008-02-03
[ "math.FA" ]
Maria Girardi, William B. Johnson
math/9301201
A Uniform Kadec-klee Property For Symmetric Operator Spaces
We show that if a rearrangement invariant Banach function space $E$ on the positive semi-axis satisfies a non-trivial lower $q-$ estimate with constant $1$ then the corresponding space $E(\nm)$ of $\tau-$measurable operators, affiliated with an arbitrary semi-finite von Neumann algebra $\nm$ equipped with a distinguish...
1993-01-28
2016-09-06
[ "math.FA" ]
Peter G. Dodds, T. K. Dodds, Paddy N. Dowling, Christopher J. Lennard, Fyodor A. Sukochev
math/9311201
The Geometry of Cycles in the Cayley Diagram of a Group
A study of triangulations of cycles in the Cayley diagrams of finitely generated groups leads to a new geometric characterization of hyperbolic groups.
1993-11-02
2008-02-03
[ "math.GR" ]
Robert H. Gilman
math/9310209
A bicombing that implies a sub-exponential isoperimetric inequality
The idea of applying isoperimetric functions to group theory is due to M.Gromov. We introduce the concept of a ``bicombing of narrow shape'' which generalizes the usual notion of bicombing. Our bicombing is related to but different from the combings defined by M. Bridson. If the Cayley graph of a group with respect to ...
1993-10-23
2008-02-03
[ "math.GR" ]
Guenther Huck and Stephan Rosebrock
math/9310207
Projective resolutions for graph products
Let $\Gamma$ be a finite graph together with a group $G_v$ at each vertex $v$. The graph product $G(\Gamma)$ is obtained from the free product of all $G_v$ by factoring out by the normal subgroup generated by $\{g^{-1}h^{-1}gh; g\in G_v, h\in G_w\}$ for all adjacent $v,w$. In this note we construct a projective resolut...
1993-10-16
2009-09-25
[ "math.GR" ]
Daniel E. Cohen
math/9310208
Isoperimetric functions for graph products
Let $\Gamma$ be a finite graph, and for each vertex $i$ let $G_i$ be a finitely presented group. Let $G$ be the graph product of the $G_i$. That is, $G$ is the group obtained from the free product of the $G_i$ by factoring out by the smallest normal subgroup containing all $[g,h]$ where $g\in G_i$ and $h\in G_j$ and th...
1993-10-16
2008-02-03
[ "math.GR" ]
Daniel E. Cohen
math/9310206
Products of Commutators and Products of Squares in a Free Group
A classification of the ways in which an element of a free group can be expressed as a product of commutators or as a product of squares is given. This is then applied to some particular classes of elements. Finally, a question about expressing a commutator as a product of squares is addressed.
1993-10-15
2008-02-03
[ "math.GR" ]
Leo P. Comerford Jr. and Charles C. Edmunds
math/9310205
Commutators as Powers in Free Products of Groups
The ways in which a nontrivial commutator can be a proper power in a free product of groups are identified.
1993-10-15
2008-02-03
[ "math.GR" ]
Leo P. Comerford Jr., Charles C. Edmunds and Gerhard Rosenberger
math/9310204
Cogrowth and essentiality in groups and algebras
The cogrowth of a subgroup is defined as the growth of a set of coset representatives which are of minimal length. A subgroup is essential if it intersects non-trivially every non-trivial subgroup. The main result of this paper is that every function $f:{\Bbb N}\cup \{0\}\rightarrow {\Bbb N}$ which is strictly increasi...
1993-10-14
2008-02-03
[ "math.GR" ]
Amnon Rosenmann
math/9310202
The Bieri-Neumann-Strebel invariants for graph groups
Given a finite simplicial graph ${\cal G}$, the graph group $G{\cal G}$" is the group with generators in one-to-one correspondence with the vertices of ${\cal G}$ and with relations stating two generators commute if their associated vertices are adjacent in ${\cal G}$. The Bieri-Neumann-Strebel invariant can be explici...
1993-10-12
2009-09-25
[ "math.GR" ]
John Meier and Leonard Vanwyk
math/9310203
Unions of Cockroft two-complexes
A combinatorial group-theoretic hypothesis is presented that serves as a necessary and sufficient condition for a union of connected Cockcroft two-complexes to be Cockcroft. This hypothesis has a component that can be expressed in terms of the second homology of groups. The hypothesis is applied to the study of the thi...
1993-10-12
2009-09-25
[ "math.GR" ]
William A. Bogley
math/9306203
Sur un generalisation del notion de producto libere amalgamate de gruppos
In ``A remark about the description of free products of groups'', Proc. Cambgridge Philos. Soc 62(1966), io ha studite lo que occurre in le circumstantia que un gruppo $G$ ha un subensemble $P$ tal que tote elemento de $G$ es representabile unicamente per un verbo reducite in $P$. Il eveni que tal $P$ es multo como un ...
1993-06-16
2016-09-06
[ "math.GR" ]
John R. Stallings
math/9306204
A note on Context Sensitive languages and Word Problems
Anisimov and Seifert show that a group has a regular word problem ifand only if it is finite. Muller and Schupp (together with Dunwoody's accessibility result) show that a group has context free word problem if and only if it is virtually free. In this note, we exhibit a class of groups where the word problem is as clo...
1993-06-16
2008-02-03
[ "math.GR" ]
Michael Shapiro
math/9306205
Automatic structures and boundaries for graphs of groups
We study the synchronous and asynchronous automatic structures on the fundamental group of a graph of groups in which each edge group is finite. Up to a natural equivalence relation, the set of biautomatic structures on such a graph product bijects to the product of the sets of biautomatic structures on the vertex grou...
1993-06-16
2008-02-03
[ "math.GR" ]
Walter D. Neumann and Michael Shapiro
math/9306202
Almost Convex Groups and the Eight Geometries
If $M$ is a closed Nil geometry 3-manifold then $\pi_1(M)$ is almost convex with respect to a fairly simple ``geometric'' generating set. If $G$ is a central extension or a ${\Bbb Z}$-extension of a word hyperbolic group, then $G$ is also almost convex with respect to some generating set. Combining these with previousl...
1993-06-16
2008-02-03
[ "math.GR" ]
Michael Shapiro and Melany Stein
math/9306201
(p,q,r)-Generations for Janko Groups $J_1$ and $J_2$
No abstract is available
1993-06-10
2009-09-25
[ "math.GR" ]
Jamshid Moori
math/9305201
Musings on Magnus
The object of this paper is to describe a simple method for proving that certain groups are residually torsion-free nilpotent, to describe some new parafree groups and to raise some new problems in honour of the memory of Wilhelm Magnus.
1993-05-26
2009-09-25
[ "math.GR" ]
Gilbert Baumslag
math/9307228
Topological invariance of intersection lattices of arrangements in CP^2
Let $\scr A^*=\{l_1,l_2,\cdots,l_n\}$ be a line arrangement in $\Bbb{CP}^2$, i.e., a collection of distinct lines in $\Bbb{CP}^2$. Let $L(\scr A^*)$ be the set of all intersections of elements of $A^*$ partially ordered by $X\leq Y\Leftrightarrow Y\subseteq X$. Let $M(\scr A^*)$ be $\Bbb{CP}^2-\bigcup\scr A^*$ where $\...
1993-07-01
2009-09-25
[ "math.GT", "math.AG" ]
Tan Jiang, Stephen S.-T. Yau
math/9307230
The genus-minimizing property of algebraic curves
A viable and still unproved conjecture states that, if $X$ is a smooth algebraic surface and $C$ is a smooth algebraic curve in $X$, then $C$ realizes the smallest possible genus amongst all smoothly embedded $2$-manifolds in its homology class. A proof is announced here for this conjecture, for a large class of surfac...
1993-07-01
2016-09-06
[ "math.GT", "math.DG" ]
Peter B. Kronheimer
math/9307233
Quasipositivity as an obstruction to sliceness
For an oriented link $L \subset S^3 = \Bd\!D^4$, let $\chi_s(L)$ be the greatest Euler characteristic $\chi(F)$ of an oriented 2-manifold $F$ (without closed components) smoothly embedded in $D^4$ with boundary $L$. A knot $K$ is {\it slice} if $\chi_s(K)=1$. Realize $D^4$ in $\C^2$ as $\{(z,w):|z|^2+|w|^2\le1\}$. It h...
1993-07-01
2008-02-03
[ "math.GT" ]
Lee Rudolph
math/9304210
Topology of homology manifolds
We construct examples of nonresolvable generalized $n$-manifolds, $n\geq 6$, with arbitrary resolution obstruction, homotopy equivalent to any simply connected, closed $n$-manifold. We further investigate the structure of generalized manifolds and present a program for understanding their topology.
1993-04-01
2009-09-25
[ "math.GT" ]
John L. Bryant, Steven C. Ferry, Washington Mio, Shmuel Weinberger
math/9304209
New points of view in knot theory
In this article we shall give an account of certain developments in knot theory which followed upon the discovery of the Jones polynomial in 1984. The focus of our account will be recent glimmerings of understanding of the topological meaning of the new invariants. A second theme will be the central role that braid the...
1993-04-01
2009-09-25
[ "math.GT" ]
Joan S. Birman
math/9301212
M\"obius invariance of knot energy
A physically natural potential energy for simple closed curves in $\bold R^3$ is shown to be invariant under M\"obius transformations. This leads to the rapid resolution of several open problems: round circles are precisely the absolute minima for energy; there is a minimum energy threshold below which knotting cannot ...
1993-01-01
2016-09-06
[ "math.GT" ]
Steve Bryson, Michael H. Freedman, Zheng-Xu He, Zhenghan Wang
math/9307227
``Theoretical mathematics'': Toward a cultural synthesis of mathematics and theoretical physics
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice there can be benefits, but there can also be unpleasant and destructive consequence...
1993-07-01
2016-09-06
[ "math.HO" ]
Arthur Jaffe, Frank Quinn
math/9301211
Representations and $K$-theory of Discrete Groups
Let $\Gamma$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $\Gamma$, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to ...
1993-01-01
2009-10-22
[ "math.KT", "math.AT" ]
Alejandro Adem
math/9312212
The number of independent elements in the product of interval Boolean algebras
We prove that in the product of kappa many Boolean algebras we cannot find an independent set of more than 2^kappa elements solving a problem of Monk (earlier it was known that we cannot find more than 2^{2^kappa} but can find 2^kappa).
1993-12-15
2016-09-06
[ "math.LO", "math.GN" ]
Saharon Shelah
math/9312204
Strong meager properties for filters
We analyze several ``strong meager'' properties for filters on the natural numbers between the classical Baire property and a filter being $F_\sigma$. Two such properties have been studied by Talagrand and a few more combinatorial ones are investigated. In particular, we define the notion of a P$^+$-filter, a generaliz...
1993-12-14
2009-09-25
[ "math.LO" ]
Claude Laflamme
math/9312203
Any behaviour of the Mitchell Ordering of Normal Measures Is Possible
Let $U_0,U_1$ be two normal measures on $\kappa .$ We say that $U_0$ is in the Mitchell ordering less then $U_1,$ $U_0\vartriangleleft U_1,$ if $U_0 \in Ult(V,U_1) .$ The ordering is well-known to be transitive and well-founded. It has been an open problem to find a model where the Mitchell ordering embeds the four-ele...
1993-12-03
2009-09-25
[ "math.LO" ]
Ji\v{r}\'i Witzany
math/9311207
Extensions of the Erd\H{o}s-Rado Theorem
We establish a variety of extensions to the Erdos-Rado Theorem, particularly involving ordinal numbers, and always involving ordinary partition relations. Most of the results can be regarded as consequences of the Ramification Principle, interpreted appropriately. Some of these problems have been open for a long time. ...
1993-11-18
2009-09-25
[ "math.LO" ]
J. Baumgartner, A. Hajnal. S. Todorcevic
math/9311212
On tree ideals
Let l^0 and m^0 be the ideals associated with Laver and Miller forcing, respectively. We show that add (l^0) < cov(l^0) and add (m^0) < cov(m^0) are consistent. We also show that both Laver and Miller forcing collapse the continuum to a cardinal <= h .
1993-11-15
2008-02-03
[ "math.LO" ]
Martin Goldstern, Miroslav Repicky, Saharon Shelah, Otmar Spinas
math/9311211
Models with second order properties, V: A General principle
We present a general framework for carrying out some constructions. The unifying factor is a combinatorial principle which we present in terms of a game in which the first player challenges the second player to carry out constructions which would be much easier in a generic extension of the universe, and the second pla...
1993-11-15
2008-02-03
[ "math.LO" ]
Bradd Hart, Claude Laflamme, Saharon Shelah
math/9311205
Applications of cohomology to questions in set theory i: hausdorff gaps
We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. The cohomology theory is introduced with enough generality to be applicable to other questions in set theory. For gaps, this leads to a natural equivalence notion about which we answer questio...
1993-11-15
2016-09-06
[ "math.LO" ]
Daniel Talayco
math/9311206
Ultrafilters on omega
A variety of classes of naturally arising ultrafilters on omega is discussed, and the question is raised whether it is consistent that the classes are empty. Since all the classes contain the P-point ultrafilters, a negative answer would greatly extend the famous theorem of Shelah.
1993-11-15
2008-02-03
[ "math.LO" ]
James E. Baumgartner
math/9311204
A combinatorial forcing for coding the universe by a real when there are no sharps
Assuming 0# does not exist, we present a combinatorial approach to Jensen's method of coding by a real. The forcing uses combinatorial consequences of fine structure (including the Covering Lemma, in various guises), but makes no direct appeal to fine structure itself.
1993-11-10
2009-09-25
[ "math.LO" ]
Saharon Shelah and Lee Stanley
math/9311203
Iterated Class Forcing
In this paper we isolate the notion of Stratified class forcing and show that Stratification implies cofinality-preservation and is preserved by iterations with the appropriate support. Many familiar class forcings are stratified and therefore can be simultaneously iterated without changing cofinalities, provided the p...
1993-11-08
2008-02-03
[ "math.LO" ]
Sy D. Friedman (MIT)
math/9311202
On hidden extenders
A model with a sequence of indiscernibles depending on a particular precovering set is constructed.The initial assumption is as follows: for every n<omega the set {alpha | o(alpha)=alpha^+n } is unbounded in kappa.
1993-11-04
2008-02-03
[ "math.LO" ]
Moti Gitik
math/9310213
IST is more than an algorithm to prove ZFC theorems
There is a sentence in the language of IST, Nelson's internal set theory, which is not equivalent in IST to a sentence in the ZFC language. Thus the Reduction algorithm of Nelson, that converts bounded IST formulas with standard parameters to provably (in IST) equivalent formulas in the ZFC language, cannot be extended...
1993-10-26
2008-02-03
[ "math.LO" ]
Vladimir Kanovei
math/9310224
Examples for Souslin forcing
We give a model where there is a ccc Souslin forcing which does not satisfy the Knaster condition. Next, we present a model where there is a sigma-linked not sigma-centered Souslin forcing such that all its small subsets are sigma-centered but Martin Axiom fails for this order. Furthermore, we construct a totally nonho...
1993-10-15
2016-09-06
[ "math.LO" ]
Haim Judah, Andrzej Ros{\l}anowski, Saharon Shelah
math/9310212
How to win some simple iteration games
We introduce two new iteration games: the game G, which is a strengthening of the weak iteration game, and the game G+, which is somewhat stronger than G but weaker than the full iteration game of length omega_1. For a countable M elementarily embeddable in some V_{eta}, we can show that II wins G(M,omega_1) and that...
1993-10-09
2008-02-03
[ "math.LO" ]
Alessandro Andretta and John R. Steel
math/9310211
Is game semantics necessary?
We discuss the extent to which game semantics is implicit in the formalism of linear logic and in the intuitions underlying linear logic.
1993-10-05
2008-02-03
[ "math.LO" ]
Andreas Blass
math/9310210
On the divisible parts of quotient groups
Techniques of combinatorial set theory are applied to the following algebraic problem. Suppose G is an abelian group such that, for all countable subgroups C, the divisible part of the quotient G/C is countable. What can one conclude about the size of the divisible part of G/K when the cardinality of the subgroup K is ...
1993-10-05
2008-02-03
[ "math.LO" ]
Andreas Blass
math/9309209
Possible Behaviours of the Reflection Ordering of Stationary Sets
If $S,T$ are stationary subsets of a regular uncountable cardinal $\kappa$, we say that $S$ reflects fully in $T$, $S<T$, if for almost all $\alpha \in T$ (except a nonstationary set) $S \cap \alpha$ is stationary in $\alpha .$ This relation is known to be a well founded partial ordering. We say that a given poset $P$ ...
1993-09-16
2016-09-06
[ "math.LO" ]
Ji\v{r}\'i Witzany
math/9309208
Questions and answers -- a category arising in linear logic, complexity theory, and set theory
A category used by de Paiva to model linear logic also occurs in Vojtas's analysis of cardinal characteristics of the continuum. Its morphisms have been used in describing reductions between search problems in complexity theory. We describe this category and how it arises in these various contexts. We also show how the...
1993-09-16
2009-09-25
[ "math.LO" ]
Andreas Blass
math/9309207
A New Proof of Kunen's Inconsistency
Using elementary pcf, we show that there is no $j:V\to M,$ $M$ transitive, $j\lambda =\lambda >crit(j),$ $j^{\prime \prime}\lambda \in M.$
1993-09-15
2008-02-03
[ "math.LO" ]
Jind\v{r}ich Zapletal
math/9309204
Evasion and prediction --- the Specker phenomenon and Gross spaces
We study the set--theoretic combinatorics underlying the following two algebraic phenomena. (1) A subgroup G leq Z^omega exhibits the Specker phenomenon iff every homomorphism G to Z maps almost all unit vectors to 0. Let se be the size of the smallest G leq Z^omega exhibiting the Specker phenomenon. (2) Given an u...
1993-09-09
2016-09-06
[ "math.LO" ]
J\"org Brendle
math/9309205
Combinatorial properties of classical forcing notions
We discuss the effect of adding a single real (for various forcing notions adding reals) on cardinal invariants associated with the continuum (like the unbounding or the dominating number or the cardinals related to measure and category on the real line). For random and Cohen forcing, this question was investigated by ...
1993-09-09
2009-09-25
[ "math.LO" ]
J\"org Brendle
math/9309206
The additivity of porosity ideals
We show that several sigma-ideals related to porous sets have additivity omega_1 and cofinality 2^omega. This answers a question addressed by Miroslav Repick'y.
1993-09-09
2009-09-25
[ "math.LO" ]
J\"org Brendle
math/9309203
Ultrafilters: Where topological dynamics = algebra = combinatorics
We survey some connections between topological dynamics, semigroups of ultrafilters, and combinatorics. As an application, we give a proof, based on ideas of Bergelson and Hindman, of the Hales-Jewett partition theorem.
1993-09-08
2009-09-25
[ "math.LO" ]
Andreas Blass
math/9308203
The structure of pleasant ideals
Normal ideals on regular uncountable cardinals are familiar objects. We investigate ideals that are pleasant--while a normal ideal is closed under arbitrary diagonal unions, a pleasant ideal is closed only under diagonal unions indexed by sets that are elements of the ideal. We show any selective ideal extending the no...
1993-08-24
2009-09-25
[ "math.LO" ]
Christopher Leary
math/9308202
Addendum to ``Maximal Chains in $\fomom$ and Ultrapowers of the Integers''
Upon presenting the proof of Theorem 3.3 in "Maximal chains in $$ and ultrapowers of the integers" I discovered that it is not entirely correct and certainly some details should be added. I have therefore written an addendum to the paper and made it available by ftp. Unfortunately the published version will be somewhat...
1993-08-20
2008-02-03
[ "math.LO" ]
Saharon Shelah, Juris Stepr\=ans
math/9308221
Universal graphs without large cliques
We give some existence/nonexistence statements on universal graphs, which under GCH give a necessary and sufficient condition for the existence of a universal graph of size lambda with no K(kappa), namely, if either kappa is finite or cf(kappa)>cf(lambda). (Here K(kappa) denotes the complete graph on kappa vertices.) T...
1993-08-15
2016-09-06
[ "math.LO" ]
Peter Komjath, Saharon Shelah
math/9308210
The canary tree
A canary tree is a tree of cardinality the continuum which has no uncountable branch, but gains a branch whenever a stationary set is destroyed (without adding reals). Canary trees are important in infinitary model theory. The existence of a canary tree is independent of ZFC + GCH.
1993-08-15
2016-09-06
[ "math.LO" ]
Alan H. Mekler, Saharon Shelah
math/9308215
Dominating functions and graphs
A graph is called dominating if its vertices can be labelled with integers in such a way that for every function f: omega-> omega the graph contains a ray whose sequence of labels eventually exceeds f. We obtain a characterization of these graphs by producing a small family of dominating graphs with the property that e...
1993-08-15
2016-09-06
[ "math.LO" ]
Reinhard Diestel, Saharon Shelah, Juris Stepr\=ans
math/9308212
On CH + 2^{aleph_1}-> (alpha)^2_2 for alpha < omega_2
We prove the consistency of ``CH + 2^{aleph_1} is arbitrarily large + 2^{aleph_1} not-> (omega_1 x omega)^2_2''. If fact, we can get 2^{aleph_1} not-> [omega_1 x omega]^2_{aleph_0}. In addition to this theorem, we give generalizations to other cardinals.
1993-08-15
2009-09-25
[ "math.LO" ]
Saharon Shelah
math/9308216
A saturated model of an unsuperstable theory of cardinality greater than its theory has the small index property
A model M of cardinality lambda is said to have the small index property if for every G subseteq Aut(M) such that [Aut(M):G] <= lambda there is an A subseteq M with |A|< lambda such that Aut_A(M) subseteq G. We show that if M^* is a saturated model of an unsuperstable theory of cardinality > Th(M), then M^* has the sma...
1993-08-15
2009-09-25
[ "math.LO" ]
Garvin Melles, Saharon Shelah
math/9308211
On a conjecture regarding nonstandard uniserial modules
We consider the question of which valuation domains (of cardinality aleph_1) have non-standard uniserial modules. We show that a criterion conjectured by Osofsky is independent of ZFC + GCH.
1993-08-15
2008-02-03
[ "math.LO", "math.RA" ]
Paul C. Eklof, Saharon Shelah
math/9308214
Somewhere trivial automorphisms
It is shown to be consistent that there is a non-trivial autohomeomorphism of beta N while all such autohomeomorphisms are trivial on some open set. The model used is one due to Velickovic in which, coincidentally, Martin's Axiom also holds.
1993-08-15
2016-09-06
[ "math.LO", "math.GN" ]
Saharon Shelah, Juris Stepr\=ans
math/9308219
Peano Arithmetic may not be interpretable in the monadic theory of orders
Gurevich and Shelah have shown that Peano Arithmetic cannot be interpreted in the monadic second-order theory of short chains (hence, in the monadic second-order theory of the real line). We show here that it is consistent that there is no interpretation even in the monadic second-order theory of all chains.
1993-08-15
2016-09-06
[ "math.LO" ]
Shmuel Lifsches, Saharon Shelah
math/9308213
On coherent systems of projections for aleph_1 separable groups
It is proved consistent with either CH or the negation of CH that there is an aleph_1-separable group of cardinality aleph_1 which does not have a coherent system of projections. It had previously been shown that it is consistent with not CH that every aleph_1-separable group of cardinality aleph_1 does have a coherent...
1993-08-15
2016-09-06
[ "math.LO", "math.RA" ]
Paul C. Eklof, Alan H. Mekler, Saharon Shelah
math/9308220
Consequences of arithmetic for set theory
In this paper, we consider certain cardinals in ZF (set theory without AC, the Axiom of Choice). In ZFC (set theory with AC), given any cardinals C and D, either C <= D or D <= C. However, in ZF this is no longer so. For a given infinite set A consider Seq(A), the set of all sequences of A without repetition. We compar...
1993-08-15
2016-09-06
[ "math.LO" ]
Lorenz Halbeisen, Saharon Shelah
math/9308217
Number of open sets for a topology with a countable basis
Let T be the family of open subsets of a topological space (not necessarily Hausdorff or even T_0). We prove that if T has a countable base and is not countable, then T has cardinality at least continuum.
1993-08-15
2008-02-03
[ "math.LO", "math.GN" ]
Saharon Shelah
math/9308218
A model in which there are Jech-Kunen trees but there are no Kurepa trees
By an omega_1 --tree we mean a tree of power omega_1 and height omega_1. We call an omega_1 --tree a Jech--Kunen tree if it has kappa --many branches for some kappa strictly between omega_1 and 2^{omega_1}. In this paper we construct the models of CH plus 2^{omega_1}> omega_2, in which there are Jech--Kunen trees and t...
1993-08-15
2016-09-06
[ "math.LO" ]
Renling Jin, Saharon Shelah
math/9308222
On uniformly antisymmetric functions
We show that there is always a uniformly antisymmetric f:A-> {0,1} if A subset R is countable. We prove that the continuum hypothesis is equivalent to the statement that there is an f:R-> omega with |S_x| <= 1 for every x in R. If the continuum is at least aleph_n then there exists a point x such that S_x has at least ...
1993-08-15
2016-09-06
[ "math.LO" ]
Peter Komjath, Saharon Shelah
math/9308201
An application of Shoenfield's absoluteness theorem to the theory of uniform distribution
If (B_x: x in N) is a Borel family of sets, indexed by the Baire space N = omega^omega, all B_x have measure zero, and the family is increasing, then the union of all B_x also has measure zero. We give two proofs of this theorem: one in the language of set theory, using Shoenfield's theorem on Sigma-1-2 sets, the other...
1993-08-06
2008-02-03
[ "math.LO" ]
Martin Goldstern
math/9306214
Strong measure zero sets without Cohen reals
If ZFC is consistent, then each of the following are consistent with ZFC + 2^{{aleph_0}}= aleph_2 : 1.) X subseteq R is of strong measure zero iff |X| <= aleph_1 + there is a generalized Sierpinski set. 2.) The union of aleph_1 many strong measure zero sets is a strong measure zero set + there is a strong measure z...
1993-06-15
2009-09-25
[ "math.LO" ]
Martin Goldstern, Haim Judah, Saharon Shelah