Supercompactness Can Be Equiconsistent with Measurability

Notre Dame Journal of Formal Logic 62 (4):593-618 (2021)
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Abstract

The main result of this paper, built on previous work by the author and T. Wilson, is the proof that the theory “ADR+DC + there is an R-complete measure on Θ” is equiconsistent with “ZF+DC+ ADR + there is a supercompact measure on ℘ω1(℘(R))+Θ is regular.” The result and techniques presented here contribute to the general program of descriptive inner model theory and in particular, to the general study of compactness phenomena in the context of ZF+DC.

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References found in this work

Proper forcing and l(ℝ).Itay Neeman & Jindřich Zapletal - 2001 - Journal of Symbolic Logic 66 (2):801-810.
Determinacy in L.Nam Trang - 2014 - Journal of Mathematical Logic 14 (1):1450006.
AD and the supercompactness of ℵ1.Howard Becker - 1981 - Journal of Symbolic Logic 46 (4):822-842.
Hod up to A D R + Θ is measurable.Rachid Atmai & Grigor Sargsyan - 2019 - Annals of Pure and Applied Logic 170 (1):95-108.
Derived models and supercompact measures on.Nam Trang - 2015 - Mathematical Logic Quarterly 61 (1-2):56-65.

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