Combined Maximality Principles up to large cardinals
Gunter Fuchs
Source: J. Symbolic Logic Volume 74, Issue 3
(2009), 1015-1046.
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1245158097
Digital Object Identifier: doi:10.2178/jsl/1245158097
Zentralblatt MATH identifier: 05609402
Mathematical Reviews number (MathSciNet): MR2548474
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