Some more Problems about Orderings of Ultrafilters

2010/05/14 by Paolo Lipparini, Lipparini, Paolo
Computer Science · Mathematics · #03C20 #03C95 #03E05 #54A20 #54D35 #54D80 #54H11 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03C20 #msc:03C95 #msc:03E05 #msc:54A20 #msc:54D35 #msc:54D80 #msc:54H11

paper · pdf · doi:10.48550/arxiv.1005.2590

7 pages

arxiv created 2010/05/14 · openalex publication_date 2010/05/14 · arxiv updated 2010/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the connection between various orders on the class of all the ultrafilters and certain compactness properties of abstract logics and of topological spaces. We present a model theoretical characterization of Comfort order. We introduce a new order motivated by considerations in abstract model theory. For each of the above orders, we show that if E is a (λ, λ)-regular ultrafilter, and D is not (λ, λ)-regular, then E \not ≤ D. Many problems are stated.

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