3 papers
math.LO2025
No covering with nowhere dense \textsf{P}-sets in the Cohen model
Alan Dow, Osvaldo Guzmán
We prove that if less than -many Cohen reals are added to a model of \textsf{CH}, then can not be covered by nowhere dense \textsf{P}-sets (equivalently, there…
math.LO2025
Ultrafilters in the random real model
Alan Dow, Osvaldo Guzmán
We prove that \textsf{P}-points (even strong P-points) and Gruff ultrafilters exist in any forcing extension obtained by adding fewer than -many random reals to a model…
math.LO2025
The Category Dichotomy for Ideals
Alan Dow, Raul Figueroa-Sierra, Osvaldo Guzmán +1
We provide a counterexample to the Category Dichotomy in the framework of . That is, we prove the existence of an ideal on that is not Katětov below $\mathsf{nwd}…