Martin’s Maximum${}^{++}$ implies Woodin’s axiom $(*)$

Pages 793-835 from Volume 193 (2021), Issue 3 by David Asperó, Ralf Schindler

Abstract

We show that Martin’s Maximum${}^{++}$ implies Woodin’s ${\mathbb P}_{\rm max}$ 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 $\aleph _2$ many real numbers.

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      title = {Forcing over models of determinacy},
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      year = {2010},
      mrclass = {03E57 (03E35 03E45 03E55 03E60 03E65)},
      mrnumber = {2768703},
      mrreviewer = {Ralf-Dieter Schindler},
      doi = {10.1007/978-1-4020-5764-9\_25},
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      fjournal = {Israel Journal of Mathematics},
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      booktitle = {Cabal Seminar 79--81},
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      number = {7},
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      pages = {504--528},
      publisher = {Hindustan Book Agency, New Delhi},
      year = {2010},
      mrclass = {03-02 (03E05 03E15 03E25 03E35 03E40 03E60)},
      mrnumber = {2827903},
      doi = {10.1142/9789814324359_0023 },
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      title = {The equivalence of {A}xiom $(*)^+$ and {A}xiom $(*)^{++}$},
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      year = {2020},
      zblnumber = {},
      }

Keywords
, , ,
Mathematical Subject Classification
Primary: , ,
DOI
https://doi.org/10.4007/annals.2021.193.3.3
MR
4250390
zbMATH
7353242
Milestones
Received: 23 May 2019
Revised: 11 May 2021
Accepted: 17 May 2021
Published online: 28 April 2021

Authors

David Asperó

University of East Anglia, Norwich, Norfolk, UK

Ralf Schindler

Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Münster, FRG