Showing papers in "Israel Journal of Mathematics in 1982"
TL;DR: In this paper, the authors present a model of set theory in which there are noP-points in βN/N and show that this model is consistent with Shelah's example.
Abstract: In this paper, we present S. Shelah's example of a model of set theory in which there are noP-points in βN/N. This settles the famous open question: “Is ‘ZFC+there are noP-points in βN/N’ consistent?”
95 citations
TL;DR: In this paper, some ideas of T. Kamae's proof using nonstandard analysis are employed to give a simple proof of Birkhoff's theorem in a classical setting as well as Kingman's subadditive ergodic theorem.
Abstract: Some ideas of T. Kamae’s proof using nonstandard analysis are employed to give a simple proof of Birkhoff’s theorem in a classical setting as well as Kingman’s subadditive ergodic theorem.
93 citations
[...]
TL;DR: For certain classes of groups, this paper showed that a map to the group of unitary transformations of a Hilbert space which is almost a homomorphism is uniformly close to a unitary representation.
Abstract: For certain classes of groups we show that a map to the group of unitary transformations of a Hilbert space which is “almost” a homomorphism is uniformly close to a unitary representation.
88 citations
TL;DR: In this article, it was shown that every finitely generated PI-algebra is polynomially bounded, where the invariants to the homogeneous identities are analogous to those of the multilinear identities studied by Regev.
Abstract: PI-algebras are studied by attaching invariants to the homogeneous identities analogous to the invariants of the multilinear identities studied by Regev. Also, it is shown that every finitely generated PI-algebra is polynomially bounded.
85 citations
TL;DR: A super-reflexive Banach space is isomorphic to a space with the property that norm-attaining operators are dense in the space of all operators into it, for any given domain space as mentioned in this paper.
Abstract: Every Banach space is isomorphic to a space with the property that the norm-attaining operators are dense in the space of all operators into it, for any given domain space. A super-reflexive space is arbitrarily nearly isometric to a space with this property.
52 citations
TL;DR: In this paper, the authors studied the dynamics of projective transformations and applied it to prove that the isotropy subgroups of probability measures on algebraic homogeneous spaces are algebraic and study the class of ergodic quasi-invariant measures of automorphisms of non-compact Lie groups.
Abstract: We study the dynamics of projective transformations and apply it to (i) prove that the isotropy subgroups of probability measures on algebraic homogeneous spaces are algebraic and to (ii) study the class of ergodic quasi-invariant measures of automorphisms of non-compact Lie groups. It is shown that their support is always a proper subset and that under certain conditions on the Lie group the induced homeomorphism of the support is topologically equivalent to a translation of a compact group.
46 citations
TL;DR: An equivelar polyhedral 2-manifold in the class M.............. p,q is one embedded in E.............. 3 in which every face is a convexp-gon and every vertex is q-valent as discussed by the authors.
Abstract: An equivelar polyhedral 2-manifold in the classM
p,q is one embedded inE
3 in which every face is a convexp-gon and every vertex isq-valent. Various constructions for equivelar manifolds are described, and it is shown that, in certain classesM
p,q, there is a manifold of given genusg≧2 for all but finitely manyg.
45 citations
TL;DR: In this article, the authors generalize the theory of Nash-Williams on well quasi-orders and better quasiorders and later results to uncountable cardinals, and find that the first cardinal κ for which some natural quasiorders are κ-well-ordered, is a (specific) mild large cardinal.
Abstract: We generalize the theory of Nash-Williams on well quasi-orders and better quasi-orders and later results to uncountable cardinals. We find that the first cardinal κ for which some natural quasi-orders are κ-well-ordered, is a (specific) mild large cardinal. Such quasi-orders are
(the class of orders which are the union of ≦λ scattered orders) ordered by embeddability and the (graph theoretic) trees under embeddings taking edges to edges (rather than to passes).
38 citations
TL;DR: In this paper, a simple proof of the individual ergodic theorem for a cyclic system with a hyperfinite cycle is given, based on the nonstandard measure theory developed by P. Loeb.
Abstract: A simple proof of the individual ergodic theorem is given. The essential tool is the nonstandard measure theory developed by P. Loeb. Any dynamical system on an abstract Lebesgue space can be represented as a factor of a “cyclic” system with a hyperfinite cycle. The ergodic theorem for such a “cyclic” system is almost trivial because of its simple structure. The general case follows from this special case.
35 citations
TL;DR: The main goal of as discussed by the authors is to complete the classification of first-order theories such that the maximum number of ℵ-saturated models in each power can be computed.
Abstract: The main goal of this paper is to complete the classification of those first-order theories such that\(I_{N_0 }^a (\lambda ,T) = 2^\lambda \). We introduce two notions, thedimensional order property anddeepness. Our main theorem asserts that for a superstable theory\(T,I_{N_{\text{0}} }^a (\lambda ,T) = 2^\lambda \) iffT has the dimensional order property or is deep. In a sense made precise in §4 this provides a syntactical characterization of theories with the maximum number of ℵɛ-saturated models in each power.
34 citations
TL;DR: In this paper, a forcing principle for regular μ>ω is shown to be equivalent to the existence of morasses, thus providing a new and systematic method for obtaining applications of morass.
Abstract: We formulate, for regular μ>ω, a “forcing principle” Sμ which we show is equivalent to the existence of morasses, thus providing a new and systematic method for obtaining applications of morasses. Various examples are given, notably that for infinitek, if 2k=k+ and there exists a (k+, 1)-morass, then there exists ak++-super-Souslin tree: a normalk++ tree characterized by a highly absolute “positive” property, and which has ak++-Souslin subtree. As a consequence we show that CH+SHℵ2⟹ℵ2 is (inaccessible)L.
TL;DR: In this paper, a set of finite symplectic, orthogonal and unitary vector spaces are used to construct strongly regular graphs having the same parameters as the perpendicularity graphs of the underlying vector spaces.
Abstract: Spreads of finite symplectic, orthogonal and unitary vector spaces are used to construct new strongly regular graphs having the same parameters as the perpendicularity graphs of the underlying vector spaces. Some of the graphs are related to partial geometries, while others produce interesting symmetric designs.
TL;DR: In this paper, a short geometric algorithm for deciding the discreteness of most 2-generator subgroups of PSL(2,R) was given, as well as a self-contained algorithmic approach to the complete classification.
Abstract: This paper gives a short geometric algorithm for deciding the discreteness of most 2-generator subgroups of PSL(2,R), as well as a self-contained algorithmic approach to the complete classification
TL;DR: A necessary and sufficient condition for the skew of the α-rotation byf (considered as taking values mod 1) to be minimal is given in this paper, and the boundedness of Σi=1nf(x+iα asn → α is resolved.
Abstract: LetT be the unit circle, α irrational andF: T → R a step function. A necessary and sufficient condition for the skew of the α-rotation byf (considered as taking values mod 1) to be minimal is given. Also, the boundedness of Σi=1nf(x+iα asn → α is resolved.
TL;DR: The existence and uniqueness results for the strict and classical solutions of the non-autonomous evolution equation under the Tanabe-Sobolevski assumptions are given in this article.
Abstract: This paper contains some existence and uniqueness results for the strict and classical solutionsu : [0,T] →E of the non-autonomous evolution equationu
1(t)=Λ(t)u(t)+f(t) in a Banach spaceE under the classical Tanabe-Sobolevski assumptions. These results do not require use of the fundamental solution and give new information about the holder-regularity of the solutions.
TL;DR: In this article, the authors studied the Banach spaces which are isomorphic to a subspace of l∞(N) which is analytic inRN. And they proved structure theorems which show that some pathological situations cannot take place in this class.
Abstract: We study the Banach spaces which are isomorphic to a subspace ofl∞(N) which is analytic inRN. We prove structure theorems which show that some pathological situations cannot take place in this class. We show that a non-metrizable separable compact of Rosenthal has a continuous image which is not a compact of Rosenthal.
TL;DR: In this paper, the authors consider different generalizations of Martin's axiom to higher cardinals, and show that a seemingly innocuous further strengthening is inconsistent with CH+2ℵ 1> ℵ2.
Abstract: We consider different generalizations of Martin’s Axiom to higher cardinals. For ℵ1, assuming CH+2ℵ 1>ℵ2+□ℵ1 we show that a generalized Martin’s Axiom considered by Baumgartner settles the ℵ2 Souslin Hypothesis ... the wrong way. We further show that, assuming CH+2ℵ 1>ℵ2, a strengthening of this axiom implies □ℵ 1. Finally, we show that a seemingly innocuous further strengthening is inconsistent with CH+2ℵ 1>ℵ2.
TL;DR: The graph of everyd-dimensional convex polytope is d-connected and contains a refinement of the complete graph ond+1 vertices as discussed by the authors, and these two theorems are generalized to pseudomanifolds and to some very general decompositions of homology manifolds.
Abstract: The graph of everyd-dimensional convex polytope isd-connected and contains a refinement of the complete graph ond+1 vertices. These two theorems are generalized to pseudomanifolds and to some very general decompositions of homology manifolds.
TL;DR: In this article, a general example of cyclic division algebra is given, based on a construction of Brauer, yielding examples of division algebras of arbitrary prime exponent without proper central subalgebra, and also noncrossed products of arbitrary exponent.
Abstract: A general example of cyclic division algebra is given, based on a construction of Brauer, yielding examples of division algebras of arbitrary prime exponent without proper central subalgebras, and also noncrossed products of arbitrary exponent.
TL;DR: In this paper, the wandering sets of a Borel automorphism are characterized as precisely those sets which have measure zero for every non-atomic measure μ which is quasi-invariant and ergodic for T.
Abstract: We characterize the wandering sets of a Borel automorphismT as being precisely those sets which have measure zero for every non-atomic measure μ which is quasi-invariant and ergodic forT.
TL;DR: In this article, a generalization of the small cancellation theory is proposed, where the usual small cancellation hypotheses are replaced by some condition that, roughly speaking, says that if a common part of two relations is a big piece of one relation then it must be a very small piece of another.
Abstract: In this paper we develop a generalization of the small cancellation theory. The usual small cancellation hypotheses are replaced by some condition that, roughly speaking, says that if a common part of two relations is a big piece of one relation then it must be a very small piece of another. In particular, we show that a finitely presented generalized small cancellation group has a solvable word problem. The machinery developed in the paper is to be used in the following papers of this series for constructing some group-theoretic examples.
TL;DR: Finite affine planes are constructed admitting nonabelian sharply point-transitive collineation groups and are of two sorts: dual translation planes and planes of type II1 derived from them as discussed by the authors.
Abstract: Finite affine planes are constructed admitting nonabelian sharply point-transitive collineation groups These planes are of two sorts: dual translation planes, and planes of type II1 derived from them
TL;DR: The authors characterizes finite groups with the property that maximal subgroups of Sylow subgroups are normal, i.e., they are all certain extensions of nilpotent groups by cyclic groups.
Abstract: This paper characterizes those finite groups with the property that maximal subgroups of Sylow subgroups are normal. They are all certain extensions of nilpotent groups by cyclic groups.
TL;DR: In this article, it was shown that polyhedral 2-manifolds cannot be homeomorphic to a closed 2-dimensional manifold, where the cardinality of the set of odd valent vertices of a polyhedron is a function of the number of facets containing a vertex.
Abstract: LetP denote a polyhedral 2-manifold, i.e. a 2-dimensional cell-complex inRd (d≧3) having convex facets, such that set (P) is homeomorphic to a closed 2-dimensional manifold. LetE be any subset of odd valent vertices ofP, andcE its cardinality. Then for the numbercP(E) of facets containing a vertex ofE the inequality 2cP(E)≧cE+1 is proved. This local combinatorial condition shows that several combinatorially possible types of polyhedral 2-manifolds cannot exist.
TL;DR: Several properties of a certain series of differential operators which are invariant under the Mobius group (Aharonov invariants) are proved, and in terms of this series new conditions for univalence and quasiconformal extendability of meromorphic functions are established as discussed by the authors.
Abstract: Several properties of a certain series of differential operators which are invariant under the Mobius group (Aharonov invariants) are proved, and in terms of this series new conditions for univalence and quasiconformal extendability of meromorphic functions are established.
TL;DR: In this paper, it was shown that ergodic automorphisms of compact abelian groups have the property that for every nonempty open set U, the measure of the set first returning to U aftern iterates decays exponentially.
Abstract: We show that ergodic automorphisms of compact abelian groups have the property that for every nonempty open setU, the measure of the set first returning toU aftern iterates decays exponentially inn. This follows from a result about aperiodic automorphisms of countable abelian groups, whose proof employsp-adic analysis.
TL;DR: In this article, the main gap for the class of models of totally transcendental first-order theories was examined, and the number of ℴ-saturated models of power ℵτ of a superstable T without the dop which is shallow but of depth ≧ω.
Abstract: We examine the main gap for the class of models of totally transcendental first-order theories, and compute the number of ℵɛ-saturated models of power ℵɛ of a superstableT without the dop which is shallow but of depth ≧ω.
TL;DR: In this article, it was shown that the theory of Frobenius fields is decidable and proved it by solving a group theoretic problem to which this question was reduced there and the notion of embedding covers of finite and pro-finite groups was developed.
Abstract: We show that the theory of Frobenius fields is decidable. This is conjectured in [4], [8] and [13], and we prove it by solving a group theoretic problem to which this question is reduced there. To do this we present and develop the notion of embedding covers of finite and pro-finite groups. We also answer two other problems from [8], again by solving a corresponding group theoretic problem: A finite extension of a Frobenius field need not be Frobenius and there are PAC fields which are not Frobenius fields.
TL;DR: In this paper, it was shown that the solution mapf→u is continuous, even if the f′s are topologized much more weakly than usual, and as a corollary the existence of solutions ofu′(t)+Au(t)∋B(u (t)), whereB is a compact mapping in a Hilbert space.
Abstract: We consideru′(t)+Au(t)∋f(t), whereA is maximal monotone in a Hilbert spaceH. AssumeA is continuous or A=ϱφ or intD(A)≠∅ or dimH<∞. For suitably boundedf′s, it is shown that the solution mapf→u is continuous, even if thef′s are topologized much more weakly than usual. As a corollary we obtain the existence of solutions ofu′(t)+Au(t)∋B(u(t)), whereB is a compact mapping inH.
TL;DR: In this article, it was shown that ifσ is a probability measure on Γ with lim supg→∞Re\(\hat \sigma \)(g)<1 (g)=1, then there exists a non-singular, properly ergodic action ofG on (X, μ) withσ(Sp(G, X))=1.
Abstract: LetG be a locally compact second countable abelian group, (X, μ) aσ-finite Lebesgue space, and (g, x) →gx a non-singular, properly ergodic action ofG on (X, μ). Let furthermore Γ be the character group ofG and let Sp(G, X) ⊂ Γ denote theL∞-spectrum ofG on (X, μ). It has been shown in [5] that Sp(G, X) is a Borel subgroup of Γ and thatσ (Sp(G, X))<1 for every probability measureσ on Γ with lim supg→∞Re\(\hat \sigma \)(g)<1, where\(\hat \sigma \) is the Fourier transform ofσ. In this note we prove the following converse: ifσ is a probability measure on Γ with lim supg→∞Re\(\hat \sigma \)(g)<1 (g)=1 then there exists a non-singular, properly ergodic action ofG on (X, μ) withσ(Sp(G, X))=1.