Borel Equivalence Relations

Borel Equivalence Relations
Author :
Publisher : American Mathematical Soc.
Total Pages : 254
Release :
ISBN-10 : 9780821844533
ISBN-13 : 0821844539
Rating : 4/5 (33 Downloads)

Synopsis Borel Equivalence Relations by : Vladimir Grigorʹevich Kanoveĭ

"Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The book presents, for the first time in mathematical literature, all major aspects of this theory and its applications."--BOOK JACKET.

Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations

Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations
Author :
Publisher : American Mathematical Soc.
Total Pages : 126
Release :
ISBN-10 : 9780821837719
ISBN-13 : 0821837710
Rating : 4/5 (19 Downloads)

Synopsis Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations by : Greg Hjorth

Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.

Classification and Orbit Equivalence Relations

Classification and Orbit Equivalence Relations
Author :
Publisher : American Mathematical Soc.
Total Pages : 217
Release :
ISBN-10 : 9780821820025
ISBN-13 : 0821820028
Rating : 4/5 (25 Downloads)

Synopsis Classification and Orbit Equivalence Relations by : Greg Hjorth

Actions of Polish groups are ubiquitous in mathematics. In certain branches of ergodic theory and functional analysis, one finds a systematic study of the group of measure-preserving transformations and the unitary group. In logic, the analysis of countable models intertwines with results concerning the actions of the infinite symmetric group. This text develops the theory of Polish group actions entirely from scratch, ultimately presenting a coherent theory of the resulting orbit equivalence classes that may allow complete classification by invariants of an indicated form. The book concludes with a criterion for an orbit equivalence relation classifiable by countable structures considered up to isomorphism. This self-contained volume offers a complete treatment of this active area of current research and develops a difficult general theory classifying a class of mathematical objects up to some relevant notion of isomorphism or equivalence.

Topics in Orbit Equivalence

Topics in Orbit Equivalence
Author :
Publisher : Springer Science & Business Media
Total Pages : 148
Release :
ISBN-10 : 3540226036
ISBN-13 : 9783540226031
Rating : 4/5 (36 Downloads)

Synopsis Topics in Orbit Equivalence by : Alexander S. Kechris

This volume provides a self-contained introduction to some topics in orbit equivalence theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and amenability. Included here are proofs of Dye's theorem that probability measure-preserving, ergodic actions of the integers are orbit equivalent and of the theorem of Connes-Feldman-Weiss identifying amenability and hyperfiniteness for non-singular equivalence relations. The presentation here is often influenced by descriptive set theory, and Borel and generic analogs of various results are discussed. The final chapter is a detailed account of Gaboriau's recent results on the theory of costs for equivalence relations and groups and its applications to proving rigidity theorems for actions of free groups.

Algebraic Ideas in Ergodic Theory

Algebraic Ideas in Ergodic Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 104
Release :
ISBN-10 : 0821889206
ISBN-13 : 9780821889206
Rating : 4/5 (06 Downloads)

Synopsis Algebraic Ideas in Ergodic Theory by : Klaus Schmidt

Descriptive Set Theory and Dynamical Systems

Descriptive Set Theory and Dynamical Systems
Author :
Publisher : Cambridge University Press
Total Pages : 304
Release :
ISBN-10 : 0521786444
ISBN-13 : 9780521786447
Rating : 4/5 (44 Downloads)

Synopsis Descriptive Set Theory and Dynamical Systems by : M. Foreman

In recent years there has been a growing interest in the interactions between descriptive set theory and various aspects of the theory of dynamical systems, including ergodic theory and topological dynamics. This volume, first published in 2000, contains a collection of survey papers by leading researchers covering a wide variety of recent developments in these subjects and their interconnections. This book provides researchers and graduate students interested in either of these areas with a guide to work done in the other, as well as with an introduction to problems and research directions arising from their interconnections.

Invariant Descriptive Set Theory

Invariant Descriptive Set Theory
Author :
Publisher : CRC Press
Total Pages : 392
Release :
ISBN-10 : 158488794X
ISBN-13 : 9781584887942
Rating : 4/5 (4X Downloads)

Synopsis Invariant Descriptive Set Theory by : Su Gao

Presents Results from a Very Active Area of ResearchExploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathem

Appalachian Set Theory

Appalachian Set Theory
Author :
Publisher : Cambridge University Press
Total Pages : 433
Release :
ISBN-10 : 9781107608504
ISBN-13 : 1107608503
Rating : 4/5 (04 Downloads)

Synopsis Appalachian Set Theory by : James Cummings

Papers based on a series of workshops where prominent researchers present exciting developments in set theory to a broad audience.

Classical and New Paradigms of Computation and their Complexity Hierarchies

Classical and New Paradigms of Computation and their Complexity Hierarchies
Author :
Publisher : Springer Science & Business Media
Total Pages : 266
Release :
ISBN-10 : 9781402027765
ISBN-13 : 1402027761
Rating : 4/5 (65 Downloads)

Synopsis Classical and New Paradigms of Computation and their Complexity Hierarchies by : Benedikt Löwe

The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies. This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.