Supercompactness Can Be Equiconsistent with Measurability

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

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.

Categories

Keywords

Reprint years

DOI

10.1215/00294527-2021-0031

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,682

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

On HOD-supercompactness.Grigor Sargsyan - 2008 - Archive for Mathematical Logic 47 (7-8):765-768.
Mouse sets.Mitch Rudominer - 1997 - Annals of Pure and Applied Logic 87 (1):1-100.
Descriptive inner model theory.Grigor Sargsyan - 2013 - Bulletin of Symbolic Logic 19 (1):1-55.
The largest countable inductive set is a mouse set.Mitch Rudominer - 1999 - Journal of Symbolic Logic 64 (2):443-459.
An Inner Model Proof of the Strong Partition Property for $delta^{2}_{1}$.Grigor Sargsyan - 2014 - Notre Dame Journal of Formal Logic 55 (4):563-568.
More on HOD-supercompactness.Arthur W. Apter, Shoshana Friedman & Gunter Fuchs - 2021 - Annals of Pure and Applied Logic 172 (3):102901.
An L-like model containing very large cardinals.Arthur W. Apter & James Cummings - 2008 - Archive for Mathematical Logic 47 (1):65-78.
Supercompactness and level by level equivalence are compatible with indestructibility for strong compactness.Arthur W. Apter - 2007 - Archive for Mathematical Logic 46 (3-4):155-163.
The consistency strength of the perfect set property for universally baire sets of reals.Ralf Schindler & Trevor M. Wilson - 2022 - Journal of Symbolic Logic 87 (2):508-526.
Indestructibility and level by level equivalence and inequivalence.Arthur W. Apter - 2007 - Mathematical Logic Quarterly 53 (1):78-85.
On measurable limits of compact cardinals.Arthur W. Apter - 1999 - Journal of Symbolic Logic 64 (4):1675-1688.
An Easton theorem for level by level equivalence.Arthur W. Apter - 2005 - Mathematical Logic Quarterly 51 (3):247-253.
Pκλ combinatorics II: The RK ordering beneath a supercompact measure.William S. Zwicker - 1986 - Journal of Symbolic Logic 51 (3):604 - 616.
Supercompactness and Measurable Limits of Strong Cardinals.Arthur W. Apter - 2001 - Journal of Symbolic Logic 66 (2):629-639.
On Measurable Limits of Compact Cardinals.Arthur Apter - 1999 - Journal of Symbolic Logic 64 (4):1675-1688.

Analytics

Added to PP
2023-01-18

Downloads
9 (#1,272,049)

6 months
5 (#693,173)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

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.

View all 6 references / Add more references