Geodesic
The Tree Property at $\omega _2$ and Bounded Forcing Axioms
Sy-David Friedman 1   ; Víctor Torres-Pérez 2
1 Kurt Gödel Research Center Universität Wien Währinger Straße 25 A-1090 Wien, Austria
2 Institut für Diskrete Mathematik und Geometrie TU Wien Wiedner Haupstraße 8/104 1040 Wien, Austria
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 3, pp. 207-216 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba8038-1-2016
Keywords: prove tree property omega together mathrm bpfa equiconsistent existence weakly compact reflecting cardinal mathrm bpfa replaced mathrm bpfa omega equiconsistent existence just weakly compact cardinal similarly special tree property omega together mathrm bpfa equiconsistent existence reflecting mahlo cardinal mathrm bpfa replaced mathrm bpfa omega equiconsistent existence just mahlo cardinal

Sy-David Friedman  1   ; Víctor Torres-Pérez  2

1 Kurt Gödel Research Center Universität Wien Währinger Straße 25 A-1090 Wien, Austria
2 Institut für Diskrete Mathematik und Geometrie TU Wien Wiedner Haupstraße 8/104 1040 Wien, Austria 
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     title = {The {Tree} {Property} at $\omega _2$ and {Bounded} {Forcing} {Axioms}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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Sy-David Friedman; Víctor Torres-Pérez. The Tree Property at $\omega _2$ and Bounded Forcing Axioms. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 3, pp. 207-216. doi: 10.4064/ba8038-1-2016

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