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On resurrection axioms

Konstantinos Tsaprounis

Journal of Symbolic Logic 80 (2):587-608 (2015)

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Identity crisis between supercompactness and vǒpenka’s principle.Yair Hayut, Menachem Magidor & Alejandro Poveda - 2022 - Journal of Symbolic Logic 87 (2):626-648.details 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. Download Export citation Bookmark
Diagonal reflections on squares.Gunter Fuchs - 2019 - Archive for Mathematical Logic 58 (1-2):1-26.details The effects of the forcing axioms \, \ and \ on the failure of weak threaded square principles of the form \\) are analyzed. To this end, a diagonal reflection principle, \, and it implies the failure of \\) if \. It is also shown that this result is sharp. It is noted that \/\ imply the failure of \\), for every regular \, and that this result is sharp as well. Download Export citation Bookmark 4 citations
Ultrahuge cardinals.Konstantinos Tsaprounis - 2016 - Mathematical Logic Quarterly 62 (1-2):77-87.details In this note, we start with the notion of a superhuge cardinal and strengthen it by requiring that the elementary embeddings witnessing this property are, in addition, sufficiently superstrong above their target. This modification leads to a new large cardinal which we call ultrahuge. Subsequently, we study the placement of ultrahugeness in the usual large cardinal hierarchy, while at the same time show that some standard techniques apply nicely in the context of ultrahuge cardinals as well. Download Export citation Bookmark 1 citation
On a class of maximality principles.Daisuke Ikegami & Nam Trang - 2018 - Archive for Mathematical Logic 57 (5-6):713-725.details We study various classes of maximality principles, \\), introduced by Hamkins :527–550, 2003), where \ defines a class of forcing posets and \ is an infinite cardinal. We explore the consistency strength and the relationship of \\) with various forcing axioms when \. In particular, we give a characterization of bounded forcing axioms for a class of forcings \ in terms of maximality principles MP\\) for \ formulas. A significant part of the paper is devoted to studying the principle MP\\) (...) Download Export citation Bookmark 1 citation
Absoluteness via resurrection.Giorgio Audrito & Matteo Viale - 2017 - Journal of Mathematical Logic 17 (2):1750005.details The resurrection axioms are forcing axioms introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Veličković. We introduce a stronger form of resurrection axioms for a class of forcings Γ and a given ordinal α), and show that RAω implies generic absoluteness for the first-order theory of Hγ+ with respect to forcings in Γ preserving the axiom, where γ = γΓ is a cardinal which depends on Γ. We also prove that the consistency strength of these axioms (...) Download Export citation Bookmark 4 citations

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