Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 74, Issue 3 (2009), 1015-1046.
Combined Maximality Principles up to large cardinals
The motivation for this paper is the following: In  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.
J. Symbolic Logic, Volume 74, Issue 3 (2009), 1015-1046.
First available in Project Euclid: 16 June 2009
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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