Generalized Descriptive Set Theory and Classification Theory
Share this pageSy-David Friedman; Tapani Hyttinen; Vadim Kulikov
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.
Table of Contents
Table of Contents
Generalized Descriptive Set Theory and Classification Theory
- Chapter 1. History and Motivation 18 free
- Chapter 2. Introduction 310 free
- Chapter 3. Borel Sets, \Dii Sets and Infinitary Logic 1320
- Chapter 4. Generalizations From Classical Descriptive Set Theory 2330
- Chapter 5. Complexity of Isomorphism Relations 5158
- Chapter 6. Reductions 5966
- Chapter 7. Open Questions 7784
- Bibliography 7986