David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Symbolic Logic 74 (3):1015-1046 (2009)
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
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Citations of this work BETA
Gunter Fuchs (2010). Generic Embeddings Associated to an Indestructibly Weakly Compact Cardinal. Annals of Pure and Applied Logic 162 (1):89-105.
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