The combinatorial essence of supercompactness

We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal. Utilizing the failure of a weak version of a square, we show that...

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Bibliographic Details
Published inAnnals of pure and applied logic Vol. 163; no. 11; pp. 1710 - 1717
Main Author Weiß, Christoph
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2012
Subjects
Ineffable
Slender
Strongly compact
Supercompact
Thin
Strongly compact
Supercompact
03E35
Ineffable
03E05
Slender
03E65
03E55
Thin
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Summary:We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal. Utilizing the failure of a weak version of a square, we show that the best currently known lower bounds for the consistency strength of these principles can be applied.
ISSN:0168-0072
DOI:10.1016/j.apal.2011.12.017