Generalized Descriptive Set Theory and Classification Theory (Memoirs of the American Mathematical Society) - Softcover

Friedman, Sy-david; Hyttinen, Tapani; Kulikov, Vadim

 
9780821894750: Generalized Descriptive Set Theory and Classification Theory (Memoirs of the American Mathematical Society)
Softcover
ISBN 10: 0821894757 ISBN 13: 9780821894750
Publisher: Amer Mathematical Society, 2014

Synopsis

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.

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About the Author

Sy-David Friedman, Kurt Godel Research Center, Vienna, Austria.Tapani Hyttinen, University of Helsinki, Finland.Vadim Kulikov, Kurt Godel Research Center, Vienna, Austria.

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Publisher
Amer Mathematical Society
Publication date
2014
Language
English
ISBN 10 
0821894757
ISBN 13 
9780821894750
Binding
Paperback
Number of pages
80