The proper forcing axiom and stationary set reflection

Type: Article

Publication Date: 1991-05-01

Citations: 19

DOI: https://doi.org/10.2140/pjm.1991.149.13

Abstract

Our main result is that the proper forcing axiom (PFA) is equiconsistent with "PFA + there is a nonreflecting stationary subset of a>2."More generally we show for any cardinals n < m < N2 that if PFA + (n) is consistent with ZFC then so is "PFA + («) + there are m mutually nonreflecting stationary subsets of ω 2 ."As corollaries we can show that if n < m < Ni then PFA + («) (if consistent) does not imply PFA + (m), and that PFA (if consistent) does not imply Martin Vs maximum.

Locations

  • Pacific Journal of Mathematics - View - PDF
  • Project Euclid (Cornell University) - View - PDF

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