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arXiv · 2507.08346

Ultrafilters in the random real model

Alan Dow·Osvaldo Guzmán
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Abstract

We prove that \textsf{P}-points (even strong P-points) and Gruff ultrafilters exist in any forcing extension obtained by adding fewer than $\aleph_{\omega}% $-many random reals to a model of \textsf{CH. }These results improve and correct previous theorems that can be found in the literature.

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Alan Dow, Osvaldo Guzmán. 2025-07-11. Ultrafilters in the random real model. https://doi.org/10.4153/s0008414x25101508

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