Journal of Symbolic Logic

Combined Maximality Principles up to large cardinals

Gunter Fuchs

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Abstract

The motivation for this paper is the following: In [4] I showed that it is inconsistent with ZFC that the Maximality Principle for directed closed forcings holds at unboundedly many regular cardinals κ (even only allowing κ itself as a parameter in the Maximality Principle for < κ-closed forcings each time). So the question is whether it is consistent to have this principle at unboundedly many regular cardinals or at every regular cardinal below some large cardinal κ (instead of ∞), and if so, how strong it is. It turns out that it is consistent in many cases, but the consistency strength is quite high.

Article information

Source
J. Symbolic Logic, Volume 74, Issue 3 (2009), 1015-1046.

Dates
First available in Project Euclid: 16 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1245158097

Digital Object Identifier
doi:10.2178/jsl/1245158097

Mathematical Reviews number (MathSciNet)
MR2548474

Zentralblatt MATH identifier
1182.03078

Citation

Fuchs, Gunter. Combined Maximality Principles up to large cardinals. J. Symbolic Logic 74 (2009), no. 3, 1015--1046. doi:10.2178/jsl/1245158097. https://projecteuclid.org/euclid.jsl/1245158097


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