Journal of Symbolic Logic

Identity Crises and Strong Compactness

Arthur W. Apter and James Cummings

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.

Abstract

Combining techniques of the first author and Shelah with ideas of Magidor, we show how to get a model in which, for fixed but arbitrary finite n, the first n strongly compact cardinals $\kappa_1,..., \kappa_n$ are so that $\kappa_i$ for i = 1,..., n is both the i$^{th}$ measurable cardinal and $\kappa^+_i$ supercompact. This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah.

Article information

Source
J. Symbolic Logic, Volume 65, Issue 4 (2000), 1895-1910.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746273

Mathematical Reviews number (MathSciNet)
MR1812190

Zentralblatt MATH identifier
0974.03044

JSTOR
links.jstor.org

Subjects
Primary: 03E35: Consistency and independence results
Secondary: 03E55: Large cardinals

Keywords
Strongly Compact Cardinal Supercompact Cardinal Measurable Cardinal Identity Crisis Reverse Easton Iteration

Citation

Apter, Arthur W.; Cummings, James. Identity Crises and Strong Compactness. J. Symbolic Logic 65 (2000), no. 4, 1895--1910. https://projecteuclid.org/euclid.jsl/1183746273


Export citation