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

2025/07/30 by Dow, Alan, Guzmán, Osvaldo
#FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.2507.22476

Abstract

We prove that if less than ℵ_ω-many Cohen reals are added to a model of \textsfCH, then ω^∗ can not be covered by nowhere dense \textsfP-sets (equivalently, there is an ultrafilter on ω that does not contain a tower).

Citations

• Ultrafilters in the random real model
• On measures induced by forcing names for ultrafilters
• Towers in filters, cardinal invariants, and Luzin type families

Related

• Adding ℵ_ω many Cohen reals
• Cardinal sequences and Cohen real extensions
• Ultrafilters with property (s)
• Adding a lot of Cohen reals by adding a few II
• Weight, net weight, and elementary submodels