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math.LO2022

Sigma-Prikry forcing III: Down to Aleph_omega

Alejandro Poveda, Assaf Rinot, Dima Sinapova

We prove the consistency of the failure of the singular cardinals hypothesis at together with the reflection of all stationary subsets of . This shows that…

math.LO2019

Sigma-Prikry forcing I: The Axioms

Alejandro Poveda, Assaf Rinot, Dima Sinapova

We introduce a class of notions of forcing which we call -Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of counta…

math.LO2019

Identity crises between supercompactness and Vopenka's Principle

Yair Hayut, Menachem Magidor, Alejandro Poveda

In this paper we study the notion of -supercompactness introduced by Bagaria in \cite{Bag} and prove the identity crises phenomenon for such class. Specifically, we show t…

math.LO2019

The tree property at first and double successors of singular cardinals with an arbitrary gap

Alejandro Poveda

Let and be a supercompact cardinal with . Assume that there is an increasing and continuous sequence of cardinals with $κ_0…