8 papers
The effects of forcing on exacting and ultraexacting cardinals
Philipp Lücke, Alejandro Poveda
Motivated by recent work of Aguilera--Bagaria--Lücke and Aguilera--Bagaria--Goldberg--Lücke (ABGL), we analyze various effects of set-theoretic forcing upon the classes of exacting…
Compactness phenomena in HOD and the Optimality of Magidor's Covering theorem
Tom Benhamou, James Cummings, Yair Hayut +2
We continue the study of compactness phenomena between the set-theoretic universe and initiated by Goldberg--Poveda \cite{GolPov}. We focus on compactness phenomena…
The number of measures on very large measurable cardinals
Arthur W. Apter, Eyal Kaplan, Alejandro Poveda
We study the possible number of normal measures on a measurable cardinal in settings where inner model techniques are unavailable. Instead, we exploit consequences of the Ultrapowe…
The directedness of the Rudin-Keisler order at measurable cardinals
Yair Hayut, Alejandro Poveda
The manuscript is concerned with the Rudin-Keisler order of ultrafilters on measurable cardinals. The main theorem proved read as follows: Given regular cardinals , the fo…
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…
On the optimality of the HOD dichotomy
Gabriel Goldberg, Jonathan Osinski, Alejandro Poveda
In the first part of the manuscript, we establish several consistency results concerning Woodin's $\HOD$ hypothesis and large cardinals around the level of extendibility. First, we…
Approximation properties of torsion classes
Sean Cox, Alejandro Poveda, Jan Trlifaj
We strengthen a result of Bagaria and Magidor~\cite{MR3152715} about the relationship between large cardinals and torsion classes of abelian groups, and prove that (1) the \emph{Ma…
Non-Normal Magidor-Radin Types of Forcings
Tom Benhamou, Alejandro Poveda
We develop the non-normal variations of two classical Prikry-type forcings; namely, Magidor and Radin forcings. We generalize the fact that the non-normal Prikry forcing is a proje…