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The Tree Property at ω2 and Bounded Forcing Axioms

Friedman S.-D., Torres-Pérez V.

Bulletin of the Polish Academy of Sciences. Mathematics

2015

Vol. 63, no. 3

207--216

We prove that the Tree Property at ω2 together with BPFA is equiconsistent with the existence of a weakly compact reflecting cardinal, and if BPFA is replaced by BPFA(ω1) then it is equiconsistent with the existence of just a weakly compact cardinal. Similarly, we show that the Special Tree Property for ω2 together with BPFA is equiconsistent with the existence of a reflecting Mahlo cardinal, and if BPFA is replaced by BPFA(ω1) then it is equiconsistent with the existence of just a Mahlo cardinal.