A Nonstandard Approach to Keisler’s Order

Graduate Thesis Or Dissertation

Citations

Citeable URL: 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.

Creator