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  1.  7
    The Tree Property at First and Double Successors of Singular Cardinals with an Arbitrary Gap.Alejandro Poveda - 2020 - Annals of Pure and Applied Logic 171 (5):102778.
  2. Sigma-Prikry Forcing II: Iteration Scheme.Alejandro Poveda, Assaf Rinot & Dima Sinapova - forthcoming - Journal of Mathematical Logic.
    In Part I of this series [5], we introduced a class of notions of forcing which we call Σ-Prikry, and showed that many of the known Prikry-type notions of forcing that centers around singular cardi...
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  3.  8
    Identity Crisis Between Supercompactness and Vǒpenka’s Principle.Yair Hayut, Menachem Magidor & Alejandro Poveda - 2022 - Journal of Symbolic Logic 87 (2):626-648.
    In this paper we study the notion of $C^{}$ -supercompactness introduced by Bagaria in [3] and prove the identity crises phenomenon for such class. Specifically, we show that consistently the least supercompact is strictly below the least $C^{}$ -supercompact but also that the least supercompact is $C^{}$ -supercompact }$ -supercompact). Furthermore, we prove that under suitable hypothesis the ultimate identity crises is also possible. These results solve several questions posed by Bagaria and Tsaprounis.
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  4.  7
    The Tree Property at Double Successors of Singular Cardinals of Uncountable Cofinality with Infinite Gaps.Mohammad Golshani & Alejandro Poveda - 2021 - Annals of Pure and Applied Logic 172 (1):102853.
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  5.  1
    Sigma-Prikry Forcing II: Iteration Scheme.Alejandro Poveda, Assaf Rinot & Dima Sinapova - forthcoming - Journal of Mathematical Logic:2150019.
    In Part I of this series [5], we introduced a class of notions of forcing which we call [Formula: see text]-Prikry, and showed that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality are [Formula: see text]-Prikry. We proved that given a [Formula: see text]-Prikry poset [Formula: see text] and a [Formula: see text]-name for a nonreflecting stationary set [Formula: see text], there exists a corresponding [Formula: see text]-Prikry poset that projects to [Formula: (...)
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