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Generalized Descriptive Set Theory and Classification Theory

Sy-David Friedman (author) Tapani Hyttinen (author)
Vadim Kulikov (author)

ISBN: 9780821894750

Publication Date: Jun 2014

Format: Paperback

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.
£63.50

Temporarily out of stock: usually despatched in 10-14 days

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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.
Pages 80
Dimensions 254 x 178
Date Published 30 Jun 2014
Publisher American Mathematical Society
Series Memoirs of the American Mathematical Society
Series Part 230/1081
Subject/s Mathematical foundations   Mathematical logic  
  • History and motivation
  • Introduction
  • Borel sets, D11 sets and infinitary logic
  • Generalizations from classical descriptive set theory
  • Complexity of isomorphism relations
  • Reductions
  • Open questions
  • Bibliography
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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