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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba8038-1-2016,
author = {Sy-David Friedman and V\'\i ctor Torres-P\'erez},
title = {The Tree Property at o2 and Bounded Forcing Axioms},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {63},
year = {2015},
pages = {207-216},
zbl = {1336.03054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba8038-1-2016}
}
Sy-David Friedman; Víctor Torres-Pérez. The Tree Property at ω₂ and Bounded Forcing Axioms. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) pp. 207-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba8038-1-2016/