Generalized descriptive set theory and classification theory
著者
書誌事項
Generalized descriptive set theory and classification theory
（Memoirs of the American Mathematical Society, no. 1081）
American Mathematical Society, 2014, c2013
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注記
"Volume 230, number 1081 (third of 5 numbers), July 2014"
Includes bibliographical references (p. 79-80)
内容説明・目次
内容説明
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.
目次
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
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