Subcompact cardinals, squares, and stationary reflection

Andrew D Brooke-Taylor, Sy-David Friedman

Research output: Contribution to journalArticle (Academic Journal)peer-review

6 Citations (Scopus)

Abstract

We generalise Jensen's result on the incompatibility of subcompactness with . We show that +-subcompactness of some cardinal less than or equal
to precludes , but also that square may be forced to hold everywhere where
this obstruction is not present. The forcing also preserves other strong large cardinals. Similar results are also given for stationary re
ection, with a corresponding strengthening of the large cardinal assumption involved. Finally, we rene the analysis by considering Schimmerling's hierarchy of weak squares, showing which cases are precluded by +-subcompactness, and again we demonstrate the optimality of our results by forcing the strongest possible squares under these restrictions to hold.
Original languageEnglish
Pages (from-to)453-473
Number of pages20
JournalIsrael Journal of Mathematics
Volume197
Issue number1
DOIs
Publication statusPublished - Oct 2013

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