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Creators/Authors contains: "Ikegami, Daisuke"

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  1. ; (, Israel Journal of Mathematics)
    Free, publicly-accessible full text available May 9, 2026
  2. ; (, Springer Proceedings in Mathematics & Statistics)
    This paper studies structural consequences of supercompact- ness of ω1 under ZF. We show that the Axiom of Dependent Choice (DC) follows from “ω1 is supercompact”. “ω1 is supercompact” also implies that AD+, a strengthening of the Axiom of Determinacy (AD), is equiv- alent to ADR. It is shown that “ω1 is supercompact” does not imply AD. The most one can hope for is Suslin co-Suslin determinacy. We show that this follows from “ω1 is supercompact” and Hod Pair Capturing (HPC), an inner-model theoretic hypothesis that imposes certain smallness con- ditions on the universe of sets. “ω1 is supercompact” on its own implies that every Suslin co-Suslin set is the projection of a determined (in fact, homogenously Suslin) set. “ω1 is supercompact” also implies all sets in the Chang model have all the usual regularity properties, like Lebesgue measurability and the Baire property. 
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    Accepted Manuscript Full Text Available
  3. ; (, Archive for Mathematical Logic)
    Full Text Available