11 papers
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 $\m…
Scales in the Point Spectrum
Tom Benhamou
We study the Point/Tukey spectrum of a general directed set using PCF theoretic tools and uncover basic connections between the theories. In particular, we prove that if the suprem…
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 \…
On the Asymptotic Behavior of Guessing Sequences
Tom Benhamou, Sean LeClair
We continue the study of probabilistic and topological properties of the set of reals that are being guessed by a diamond sequence from \cite{Benhamou_Wu}. We show that the existen…
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 i…
Commutativity of Cofinal Types
Tom Benhamou
We continue the study of the pseudo-intersection property with respect to an ideal introduced in \cite{TomNatasha2}. Our theory applies to the study of the Tukey types of general s…