## Journal of Symbolic Logic

### Identity Crises and Strong Compactness

#### 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 This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah.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

https://projecteuclid.org/euclid.jsl/1183746273

Mathematical Reviews number (MathSciNet)
MR1812190

Zentralblatt MATH identifier
0974.03044

JSTOR