The Tree Property at ω₂ and Bounded Forcing Axioms

• Autorzy: Sy-David Friedman , Víctor Torres-Pérez
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E65: Other hypotheses and axioms
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: 63
• Numer: 3
• Strony: 207-216

Daty

wydano

2015

Twórcy

autor

Sy-David Friedman

• Kurt Gödel Research Center, Universität Wien, Währinger Straße 25, A-1090 Wien, Austria

autor

Víctor Torres-Pérez

• Institut für Diskrete Mathematik und Geometrie, TU Wien, Wiedner Haupstraße 8/104, 1040 Wien, Austria

Identyfikatory

DOI

10.4064/ba8038-1-2016