Generalized Descriptive Set Theory and Classification Theory

Cover
American Mathematical Soc., 05.06.2014 - 80 Seiten

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.

 

Ausgewählte Seiten

Inhalt

Chapter 1 History and Motivation
1
Chapter 2 Introduction
3
Chapter 3 Borel Sets Dii Sets and Infinitary Logic
13
Chapter 4 Generalizations From Classical Descriptive Set Theory
23
Chapter 5 Complexity of Isomorphism Relations
51
Chapter 6 Reductions
59
Chapter 7 Open Questions
77
Bibliography
79
Urheberrecht

Häufige Begriffe und Wortgruppen

AMS-LATEX arbitrary Assume assumption basic open sets bijection Borel reducibility Borel sets classifiable and shallow Clearly closed set closed under permutations co-meager cofinality complement countable cub set definition dense Department of Mathematics descriptive set theory downward closed e-mail element elementary submodel equivalence classes equivalence relation exists first-order forcing extension function Hyttinen implies increasing sequence initial segment isomorphism relation Kurepa tree Lemma Let f Let G Let us define Let us show limit ordinal linear order modulo non-stationary Open Problem order type OTOP P-generic partial isomorphism Proof of Claim Proof of item proof of Theorem Property of Baire ran Fo reduction regular cardinal S C R satisfies sentence Silver Dichotomy sprt stable unsuperstable stationary set stationary subset strategy of player successor superstable Suppose uncountable vocabulary w-tree winning strategy κκ

Bibliografische Informationen

TitelGeneralized Descriptive Set Theory and Classification Theory
Memoirs of the American Mathematical Society
AutorenSy-David Friedman, Tapani Hyttinen, Vadim Kulikov
VerlagAmerican Mathematical Soc., 2014
ISBN0821894757, 9780821894750
Länge80 Seiten
  
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