arXiv:1012.2040 Abstract | arXiv Analytics

arXiv:1012.2040 [math.LO]Abstract References Reviews Resources

The combinatorial essence of supercompactness

Published 2010-12-09Version 1

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 square, we show that the best currently known lower bounds for the consistency strength of these principles can be applied.

Categories: math.LO

Subjects: 03E05, 03E35, 03E55, 03E65

Keywords: combinatorial essence, supercompactness, combinatorial principles, consistency strength, characterize strong compactness

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