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On the consistency strength of the proper forcing axiom
2011
Advances in Mathematics
In recent work, the second author extended combinatorial principles due to Jech and Magidor that characterize certain large cardinal properties so that they can also hold true for small cardinals. For inaccessible cardinals, these modifications have no effect, and the resulting principles still give the same characterization of large cardinals. We prove that the proper forcing axiom PFA implies these principles hold for ω 2 . Using this, we argue to show that any of the known methods for
doi:10.1016/j.aim.2011.07.016
fatcat:jb4iwnxqevcazbeo7wzkvufmym