On regular ultrafilters, Boolean ultrapowers, and Keisler's order
Francesco Parente
TL;DR
This paper compares two notions of regularity for filters on Boolean algebras and links Boolean ultrapowers to Keisler's order, advancing the understanding of model-theoretic classification.
Contribution
It introduces a comparison of regularity notions and characterizes Keisler's order using Boolean ultrapowers, offering new insights into model theory.
Findings
Comparison of two regularity notions for filters
Characterization of Keisler's order via Boolean ultrapowers
Two results announced for future publication
Abstract
In this paper we analyse and compare two different notions of regularity for filters on complete Boolean algebras. We also announce two results from a forthcoming paper in preparation, which provide a characterization of Keisler's order in terms of Boolean ultrapowers.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Algebra and Logic · Advanced Topology and Set Theory