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Double helix in large large cardinals and iteration of elementary embeddings

Kentaro Sato

Annals of Pure and Applied Logic 146 (2):199-236 (2007)

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More on HOD-supercompactness.Arthur W. Apter, Shoshana Friedman & Gunter Fuchs - 2021 - Annals of Pure and Applied Logic 172 (3):102901.details We explore Woodin's Universality Theorem and consider to what extent large cardinal properties are transferred into HOD (and other inner models). We also separate the concepts of supercompactness, supercompactness in HOD and being HOD-supercompact. For example, we produce a model where a proper class of supercompact cardinals are not HOD-supercompact but are supercompact in HOD. Additionally we introduce a way to measure the degree of HOD-supercompactness of a supercompact cardinal, and we develop methods to control these degrees simultaneously for a (...) Download Export citation Bookmark
Indestructibility of Vopěnka’s Principle.Andrew D. Brooke-Taylor - 2011 - Archive for Mathematical Logic 50 (5-6):515-529.details Vopěnka’s Principle is a natural large cardinal axiom that has recently found applications in category theory and algebraic topology. We show that Vopěnka’s Principle and Vopěnka cardinals are relatively consistent with a broad range of other principles known to be independent of standard (ZFC) set theory, such as the Generalised Continuum Hypothesis, and the existence of a definable well-order on the universe of all sets. We achieve this by showing that they are indestructible under a broad class of forcing constructions, (...) Download Export citation Bookmark 6 citations
A new model construction by making a detour via intuitionistic theories III: Ultrafinitistic proofs of conservations of Σ 1 1 collection. [REVIEW]Kentaro Sato - 2023 - Annals of Pure and Applied Logic 174 (3):103207.details Download Export citation Bookmark 1 citation

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