## Journal of the Mathematical Society of Japan

### On the level by level equivalence between strong compactness and strongness

Arthur W. APTER

#### Abstract

We construct a model in which the least strongly compact cardinal $\kappa$ is also the least strong cardinaj $\kappa$ isn't $2^{\kappa}$ supercompact, and for any $\delta<\kappa$, if $\delta^{+\alpha}$ is regular, $\delta$ is $\delta^{+\alpha}$ strongly compact if and only if $\delta$ is $\delta+\alpha+1$ strong.

#### Article information

Source
J. Math. Soc. Japan, Volume 55, Number 1 (2003), 47-58.

Dates
First available in Project Euclid: 5 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1196890841

Digital Object Identifier
doi:10.2969/jmsj/1196890841

Mathematical Reviews number (MathSciNet)
MR1939184

Zentralblatt MATH identifier
1029.03038

#### Citation

W. APTER, Arthur. On the level by level equivalence between strong compactness and strongness. J. Math. Soc. Japan 55 (2003), no. 1, 47--58. doi:10.2969/jmsj/1196890841. https://projecteuclid.org/euclid.jmsj/1196890841