The relation of rapid ultrafilters and Q-points to van der Waerden ideal

2010/04/12 by Jana Flašková, Flašková, Jana
Mathematics · #54D40 #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Primary 03E05 #Rings, Modules, and Algebras #Secondary 03E75

paper · pdf · doi:10.48550/arxiv.1004.1879

openalex publication_date 2010/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We point out one of the differences between rapid ultrafilters and Q-points: Rapid ultrafilters may have empty intersection with van der Waerden ideal, whereas every Q-point has a non-empty intersection with van der Waerden ideal. Assuming Martin's axiom for countable posets we also construct a W-ultrafilter which is not a Q-point.

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