The Tree Property at $\omega _2$ and Bounded Forcing Axioms

Volume 63 / 2015

Sy-David Friedman, Víctor Torres-Pérez Bulletin Polish Acad. Sci. Math. 63 (2015), 207-216 MSC: Primary 03E35; Secondary 03E65. DOI: 10.4064/ba8038-1-2016 Published online: 19 January 2016

Abstract

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.

Authors

  • Sy-David FriedmanKurt Gödel Research Center
    Universität Wien
    Währinger Straße 25
    A-1090 Wien, Austria
    e-mail
  • Víctor Torres-PérezInstitut für Diskrete Mathematik und Geometrie
    TU Wien
    Wiedner Haupstraße 8/104
    1040 Wien, Austria
    e-mail

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