Alan Dow

most citedUltrafilters in the random real model

1 citations · 2 across the 4 of their papers we have counts for

collaborators

4 papers

math.LO2026

Nontrivial automorphisms of $P (ω) / Fin$ in Cohen models

Will Brian, Alan Dow

We show that if $κ < ℵ_{ω}$ Cohen reals are added to a model of $CH$ , then there are nontrivial automorphisms of $P (ω) / Fin$ in the extension. Under som…

math.LO2025

No covering with nowhere dense \textsf{P}-sets in the Cohen model

Alan Dow, Osvaldo Guzmán

We prove that if less than $ℵ_{ω}$ -many Cohen reals are added to a model of \textsf{CH}, then $ω^{*}$ can not be covered by nowhere dense \textsf{P}-sets (equivalently, there…

math.LO2025★ 1 cited

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 $ℵ_{ω}$ -many random reals to a model…

math.LO2025★ 1 cited

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 $ZFC$ . That is, we prove the existence of an ideal on $ω$ that is not Katětov below $\mathsf{nwd}…

Nontrivial automorphisms of P(ω)/Fin in Cohen models

No covering with nowhere dense \textsf{P}-sets in the Cohen model

Ultrafilters in the random real model

The Category Dichotomy for Ideals

Nontrivial automorphisms of $P (ω) / Fin$ in Cohen models