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The proper forcing
axiom and stationary set reflection
Robert Emile Beaudoin |
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Vol. 149 (1991), No. 1, 13–24
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Abstract |
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Our main result is that the proper forcing axiom (PFA) is equiconsistent with “PFA + there is a nonreflecting stationary subset of ω2”. More generally we show for any cardinals n < m ≤ℵ2 that if PFA+(n) is consistent with ZFC then so is “PFA+(n) + there are m mutually nonreflecting stationary subsets of ω2”. As corollaries we can show that if n < m ≤ℵ1 then PFA+(n) (if consistent) does not imply PFA+(m), and that PFA (if consistent) does not imply Martin’s maximum. |
Mathematical Subject Classification 2000
Primary: 03E35
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Milestones
Received: 29 August 1989
Published: 1 May 1991
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Authors |
| Robert Emile Beaudoin | |
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