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University of Illinois – Chicago

1. Sahota, Davender S. Borel Complexity of the Isomorphism Relation for O-minimal Theories.

Degree: 2013, University of Illinois – Chicago

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. Advisors/Committee Members: Marker, David E. (advisor), Baldwin, John T. (committee member), Goldbring, Isaac (committee member), Rosendal, Christian (committee member), Laskowski, Michael C. (committee member).

Subjects/Keywords: Model Theory; Descriptive Set Theory; O-minimal; Borel complete; Vaught's Conjecture

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Sahota, D. S. (2013). Borel Complexity of the Isomorphism Relation for O-minimal Theories. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/10171

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Sahota, Davender S. “Borel Complexity of the Isomorphism Relation for O-minimal Theories.” 2013. Thesis, University of Illinois – Chicago. Accessed August 08, 2020. http://hdl.handle.net/10027/10171.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Sahota, Davender S. “Borel Complexity of the Isomorphism Relation for O-minimal Theories.” 2013. Web. 08 Aug 2020.

Vancouver:

Sahota DS. Borel Complexity of the Isomorphism Relation for O-minimal Theories. [Internet] [Thesis]. University of Illinois – Chicago; 2013. [cited 2020 Aug 08]. Available from: http://hdl.handle.net/10027/10171.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sahota DS. Borel Complexity of the Isomorphism Relation for O-minimal Theories. [Thesis]. University of Illinois – Chicago; 2013. Available from: http://hdl.handle.net/10027/10171

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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