Realization of φ-types and Keisler’s order

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Abstract

We show that the analysis of Keisler’s order can be localized to the study of φ-types. Specifically, if D is a regular ultrafilter on λ such that lcf(ω,D)λ+ and M is a model whose theory is countable, then Mλ/D is λ+-saturated iff it realizes all φ-types of size λ.

MSC

03C95
03C20

Keywords

Saturation of ultrapowers
Keisler’s order
Unstable theories
Regular filters

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