Martin's Maximum++ implies Woodin's axiom (*)

David Aspero, Ralf Schindler

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Abstract

We show that Martin's Maximum ++ implies Woodin's Pmax axiom (*). This answers a question from the 1990s and amalgamates two prominent axioms of set theory which were both known to imply that there are N2 many real numbers.

Original languageEnglish
Pages (from-to)793-835
Number of pages43
JournalAnnals of Mathematics
Volume193
Issue number3
DOIs
Publication statusPublished - May 2021

Keywords

  • $\mathbb P_{max}$, Continuum Hypothesis, Axiom $(*)$, forcing axioms

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