Bounded Martin’s Maximum with an Asterisk

David Asperó, Ralf Schindler

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Abstract

We isolate natural strengthenings of Bounded Martin’s Maximum which we call BMM∗BMM∗ and A−BMM∗,++A−BMM∗,++ (where AA is a universally Baire set of reals), and we investigate their consequences. We also show that if A−BMM∗,++A−BMM∗,++ holds true for every set of reals AA in L(R)L(R), then Woodin’s axiom (∗)(∗) holds true. We conjecture that MM++MM++ implies A−BMM∗,++A−BMM∗,++ for every AA which is universally Baire.
Original languageEnglish
Pages (from-to)333-348
Number of pages16
JournalNotre Dame Journal of Formal Logic
Volume55
Issue number3
Early online date22 Jul 2014
DOIs
Publication statusPublished - 2014

Keywords

  • BMM∗
  • A−BMM∗,++
  • honestly consistent statement
  • Pmax

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