11 citations · 11 across the 14 of their papers we have counts for
14 papers · 1 filter
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…
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…
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…
Stationary Reflection and the Failure OF SCH at
Tom Benhamou, Dima Sinapova
Combining stationary reflection (a compactness property) with the failure of SCH (an instance of non-compactness) has been a long-standing theme. We obtain this at ,…
On Ultrapowers and Cohesive Ultrafilters
Tom Benhamou
We characterize the Tukey order, the Galvin property/ Cohesive ultrafilters from \cite{Kanamori1978} in terms of ultrapowers. We use this characterization to measure the distance b…
Diamond principles and Tukey-top ultrafilters on a countable set
Tom Benhamou, Fanxin Wu
We provide two types of guessing principles for ultrafilter () on which form subclasses of Tukey-top ultrafilters, and construct s…
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…
A Small Ultrafilter Number at Every Singular Cardinal
Tom Benhamou, Sittinon Jirattikansakul
We obtain a small ultrafilter number at . Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal …
Prikry Forcing and Tree Prikry Forcing of Various Filters
Tom Benhamou
In this paper, we answer a question asked in "A minimal Prikry type forcing for singularizing a measurable cardinal" regarding a Mathias criteria for Tree-Prikry forcing. Also we w…