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You searched for +publisher:"University of Illinois – Chicago" +contributor:("Baldwin, John T."). Showing records 1 – 2 of 2 total matches.

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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

2. Drueck, Fred R. Limit Models, Superlimit Models, and Two Cardinal Problems in Abstract Elementary Classes.

Degree: 2013, University of Illinois – Chicago

This dissertation examines three main topics, the topic of defining "superstability" for abstract elementary classes (AECs), uniqueness of limit models, and two cardinal models in abstract elementary classes. In particular we further generalize an analogue of Vaught's theorem which constructs an uncountable two cardinal model starting from the existence of a countable Vaughtian pair in an elementary class to the AEC context originally published by Lessmann, who in turn built upon the work of Grossberg and VanDieren, Shelah, and others. We also give various sufficient conditions on countable models, as well as a condition on models of size kappa that, assuming that a simplified morass,ñ allows us to construct a (kappa^++,kappa)-model. We discuss how this work in AECs to some degree parallels the proof of Jensen's Gap-2 transfer theorem for elementary classes. We also discuss difficulties inherent in proving a true gap-2 transfer theorem for AECs. Additionally, we discuss, progress that has been made toward proving the uniqueness of limit models assuming various "superstability-like" assumptions (much of the work described is due to Shelah, Villaveces, Grossberg, and VanDieren). One small original result is contributed to this discussion. Advisors/Committee Members: Baldwin, John T. (advisor), Marker, David (committee member), Takloo-Bighash, Ramin (committee member), VanDieren, Monica (committee member), Scow, Lynn (committee member).

Subjects/Keywords: Limit Models; Superlimit Models; Two Cardinal Problems; two cardinal models; two cardinal; 2 cardinal; 2 cardinal problems; 2 cardinal model; gap-2 transfer; gap-2; Abstract Elementary Classes; mathematical logic; uniqueness of limit models; morasses; lessmann

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

APA (6th Edition):

Drueck, F. R. (2013). Limit Models, Superlimit Models, and Two Cardinal Problems in Abstract Elementary Classes. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/9996

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):

Drueck, Fred R. “Limit Models, Superlimit Models, and Two Cardinal Problems in Abstract Elementary Classes.” 2013. Thesis, University of Illinois – Chicago. Accessed August 08, 2020. http://hdl.handle.net/10027/9996.

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

MLA Handbook (7th Edition):

Drueck, Fred R. “Limit Models, Superlimit Models, and Two Cardinal Problems in Abstract Elementary Classes.” 2013. Web. 08 Aug 2020.

Vancouver:

Drueck FR. Limit Models, Superlimit Models, and Two Cardinal Problems in Abstract Elementary Classes. [Internet] [Thesis]. University of Illinois – Chicago; 2013. [cited 2020 Aug 08]. Available from: http://hdl.handle.net/10027/9996.

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

Council of Science Editors:

Drueck FR. Limit Models, Superlimit Models, and Two Cardinal Problems in Abstract Elementary Classes. [Thesis]. University of Illinois – Chicago; 2013. Available from: http://hdl.handle.net/10027/9996

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

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