Graduate Thesis Or Dissertation
A Nonstandard Approach to Keisler’s Order Public Deposited
https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/w0892c69h
- Abstract
We use the methods of model-theoretic nonstandard analysis, in particular enlargements, to study the properties of regular and good ultrafilters and their role within Keisler's order on countable complete first-order theories. This understanding is used to produce alternative proofs of several key theorems in the study of Keisler's order, such as the well-definedness of Keisler's order and the maximality of theories with SOP2 (Strict Order Property 2). Furthermore, we provide an analysis of the logical structure of the types used in the proof that theories with SOP2 are Keisler maximal and use this analysis to give an easy-to-state set-theoretic characterization of ultrafilters that are both regular and good.
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- Date Issued
- 2023-04-16
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- Last Modified
- 2024-01-04
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Wheeler_colorado_0051E_18211.pdf | 2023-12-15 | Public | Download |
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Thesis_Approval_Form.pdf | 2023-12-15 | Public | Download |