Alan Dow

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4 papers · 1 filter

math.LO2026

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

Will Brian, Alan Dow

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

math.LO2025

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

Alan Dow, Osvaldo GuzmÃ¡n

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

math.LO2025

Ultrafilters in the random real model

Alan Dow, Osvaldo GuzmÃ¡n

We prove that \textsf{P}-points (even strong P-points) and Gruff ultrafilters exist in any forcing extension obtained by adding fewer than $ℵ_{I ¨} $ -many random reals to a mode…

math.LO2025

The Category Dichotomy for Ideals

Alan Dow, Raul Figueroa-Sierra, Osvaldo GuzmÃ¡n +1

We provide a counterexample to the Category Dichotomy in the framework of $ZFC$ . That is, we prove the existence of an ideal on $I ¨ $ that is not KatÄtov below $\mathsf{nw…

Nontrivial automorphisms of P(I¨)/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 $P (I ¨ ) / Fin$ in Cohen models