Dissertation/Thesis Abstract

Borel Complexity of the Isomorphism Relation for O-minimal Theories
by Sahota, Davender Singh, Ph.D., University of Illinois at Chicago, 2013, 61; 3604080
Abstract (Summary)

In 1988, Mayer published a strong form of Vaught's Conjecture for o-minimal theories. She showed Vaught's Conjecture holds, and characterized the number of countable models of an o-minimal theory T if T has fewer than continuum many countable models. Friedman and Stanley have shown that several elementary classes are Borel complete. In this thesis we address the class of countable models of an o-minimal theory T when T has continuum many countable models. Our main result gives a model theoretic dichotomy describing the Borel complexity of isomorphism on the class of countable models of T. The first case is if T has no simple types, isomorphism is Borel on the class of countable models of T. In the second case, T has a simple type over a finite set A, and there is a finite set B containing A such that the class of countable models of the completion of T over B is Borel complete.

Indexing (document details)
Advisor: Marker, David
Commitee: Marker, David E.
School: University of Illinois at Chicago
Department: Mathematics, Statistics, and Computer Science
School Location: United States -- Illinois
Source: DAI-B 75/03(E), Dissertation Abstracts International
Subjects: Logic, Mathematics, Theoretical Mathematics
Keywords: Borel complete, Descriptive set theory, Model theory, O-minimal, Vaught's conjecture
Publication Number: 3604080
ISBN: 978-1-303-59366-6
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