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math.LO2024
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…
math.LO2024
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…
math.LO2024
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…