Ultrafilters in the random real model

2025/07/11 by Dow, Alan, Guzmán, Osvaldo · 1 citation
#03E05 #03E17 #03E35 #03E65 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2507.08346

Abstract

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

Citations

• The ultrafilter and almost disjointness numbers
• Pseudo P-points and splitting number
• There are no P-points in Silver extensions
• Bounding, splitting, and almost disjointness

Cited by

• No covering with nowhere dense \textsfP-sets in the Cohen model

Related

• A unique Q-point and infinitely many near-coherence classes of ultrafilters
• The next best thing to a P-point
• Isomorphism Classes of Generating Sets
• Model-theoretic properties of ultrafilters built by independent families of functions
• Pseudo P-points and splitting number