11 citations · 11 across the 14 of their papers we have counts for
6 papers · 2 filters
Eventual Capture on a Measurable Cardinal
Tom Benhamou, Corey Bacal Switzer
We continue the study from \cite{BrendleFreidmanMontoya, vandervlugtlocalizationcardinals} of localization cardinals $\mfb_κ(\in^*)$ and $\mfd_κ(\in^*)$ and their variants at regul…
Supercompact Measures and the Galvin Property
Tom Benhamou, Ben-Zion Weltsch
We study saturation properties of -complete measures on , where can be either regular or singular. In particular, we prove that in contrast to Galvin's theorem, the…
Ultrafilters over Successor Cardinals and the Tukey Order
Tom Benhamou, Justin T. Moore, Luke Serafin
We study ultrafilters on regular uncountable cardinals, with a primary focus on , and particularly in relation to the Tukey order on directed sets. Results include the indepen…
Isomorphism Classes of Generating Sets
Tom Benhamou, James Cummings, Gabriel Goldberg +2
We introduce a new class of ultrafilters which generalizes the well-known class of simple -point ultrafilters. We prove that for any well-founded -directed partial order $\ma…
Cardinals of the -Filter Games
Tom Benhamou, Victoria Gitman
We investigate forms of filter extension properties in the two-cardinal setting involving filters on . We generalize the filter games introduced by Holy and Schlicht in \ci…
Measures that violate the Generalized Continuum Hypothesis
Tom Benhamou, Gabriel Goldberg
A simple \(P_λ\)-point on a regular cardinal \(κ\) is a uniform ultrafilter on \(κ\) with a mod-bounded decreasing generating sequence of length \(λ\). We prove that if there is a…