November 2021 Supercompactness Can Be Equiconsistent with Measurability
Nam Trang
Author Affiliations +
Notre Dame J. Formal Logic 62(4): 593-618 (November 2021). DOI: 10.1215/00294527-2021-0031

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.

Citation

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Nam Trang. "Supercompactness Can Be Equiconsistent with Measurability." Notre Dame J. Formal Logic 62 (4) 593 - 618, November 2021. https://doi.org/10.1215/00294527-2021-0031

Information

Received: 6 June 2019; Accepted: 22 May 2021; Published: November 2021
First available in Project Euclid: 13 December 2021

MathSciNet: MR4350949
zbMATH: 07473061
Digital Object Identifier: 10.1215/00294527-2021-0031

Subjects:
Primary: 03E45
Secondary: 03E15 , 03E60

Keywords: descriptive set theory , hod mouse , inner model theory , Mouse , supercompactness on ω1

Rights: Copyright © 2021 University of Notre Dame

Vol.62 • No. 4 • November 2021
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