A unique Q-point and infinitely many near-coherence classes of ultrafilters

2025/05/23 by Lorenz Halbeısen, Halbeisen, Lorenz, Saharon Shelah +2 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Harmonic Analysis Research #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2505.17960

Abstract

We show that in the model obtained by iteratively pseudo-intersecting a Ramsey ultrafilter via a length-ω₂ countable support iteration of restricted Mathias forcing over a ground model satisfying \textsfCH, there is a unique Q-point up to isomorphism. In particular, it is consistent that there is only one Q-point while there are 2^\mathfrakc-many near-coherence classes of ultrafilters.

Cited by

• There may be exactly n Q-points

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