Bulletin of Symbolic Logic

Gap Forcing: Generalizing the Lévy-Solovay Theorem

Joel David Hamkins

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

Abstract

The Lévy-Solovay Theorem [8] limits the kind of large cardinal embeddings that can exist in a small forcing extension. Here I announce a generalization of this theorem to a broad new class of forcing notions. One consequence is that many of the forcing iterations most commonly found in the large cardinal literature create no new weakly compact cardinals, measurable cardinals, strong cardinals, Woodin cardinals, strongly compact cardinals, supercompact cardinals, almost huge cardinals, huge cardinals, and so on.

Article information

Source
Bull. Symbolic Logic, Volume 5, Number 2 (1999), 264-272.

Dates
First available in Project Euclid: 20 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1182353622

Mathematical Reviews number (MathSciNet)
MR1792281

Zentralblatt MATH identifier
0933.03067

JSTOR
links.jstor.org

Citation

Hamkins, Joel David. Gap Forcing: Generalizing the Lévy-Solovay Theorem. Bull. Symbolic Logic 5 (1999), no. 2, 264--272. https://projecteuclid.org/euclid.bsl/1182353622


Export citation