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Generalized Descriptive Set Theory and Classification Theory

2014-10-03 MATHEMATICS
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Release : 2014-10-03
Genre : MATHEMATICS
Kind : eBook
Book Rating : 713/5 ( reviews)

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Book Synopsis Generalized Descriptive Set Theory and Classification Theory by : Sy D. Friedman

Download or read book Generalized Descriptive Set Theory and Classification Theory written by Sy D. Friedman. This book was released on 2014-10-03. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Generalized Descriptive Set Theory and Classification Theory

2014-06-05 Mathematics
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Release : 2014-06-05
Genre : Mathematics
Kind : eBook
Book Rating : 757/5 ( reviews)

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Book Synopsis Generalized Descriptive Set Theory and Classification Theory by : Sy-David Friedman

Download or read book Generalized Descriptive Set Theory and Classification Theory written by Sy-David Friedman. This book was released on 2014-06-05. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

A Homology Theory for Smale Spaces

2014-09-29 Mathematics
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Release : 2014-09-29
Genre : Mathematics
Kind : eBook
Book Rating : 097/5 ( reviews)

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Book Synopsis A Homology Theory for Smale Spaces by : Ian F. Putnam

Download or read book A Homology Theory for Smale Spaces written by Ian F. Putnam. This book was released on 2014-09-29. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.

Local Entropy Theory of a Random Dynamical System

2014-12-20 Mathematics
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Release : 2014-12-20
Genre : Mathematics
Kind : eBook
Book Rating : 559/5 ( reviews)

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Book Synopsis Local Entropy Theory of a Random Dynamical System by : Anthony H. Dooley

Download or read book Local Entropy Theory of a Random Dynamical System written by Anthony H. Dooley. This book was released on 2014-12-20. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.

Descriptive Set Theory and the Structure of Sets of Uniqueness

1987-11-27 Mathematics
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Release : 1987-11-27
Genre : Mathematics
Kind : eBook
Book Rating : 118/5 ( reviews)

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Book Synopsis Descriptive Set Theory and the Structure of Sets of Uniqueness by : A. S. Kechris

Download or read book Descriptive Set Theory and the Structure of Sets of Uniqueness written by A. S. Kechris. This book was released on 1987-11-27. Available in PDF, EPUB and Kindle. Book excerpt: To make this work accessible to logicians as well as set theorists and analysts, classical and modern theory of sets of uniqueness are covered as well as the relevant parts of descriptive set theory.

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