The Tree Property at and Bounded Forcing Axioms
Tom 63 / 2015
Bulletin Polish Acad. Sci. Math. 63 (2015), 207-216
MSC: Primary 03E35; Secondary 03E65.
DOI: 10.4064/ba8038-1-2016
Opublikowany online: 19 January 2016
Streszczenie
We prove that the Tree Property at \omega _2 together with \mathrm {BPFA} is equiconsistent with the existence of a weakly compact reflecting cardinal, and if \mathrm {BPFA} is replaced by \mathrm {BPFA}(\omega _1) then it is equiconsistent with the existence of just a weakly compact cardinal. Similarly, we show that the Special Tree Property for \omega _2 together with \mathrm {BPFA} is equiconsistent with the existence of a reflecting Mahlo cardinal, and if \mathrm {BPFA} is replaced by \mathrm {BPFA}(\omega _1) then it is equiconsistent with the existence of just a Mahlo cardinal.
