Bounded Martin’s Maximum with an Asterisk

Asperó, David and Schindler, Ralf (2014) Bounded Martin’s Maximum with an Asterisk. Notre Dame Journal of Formal Logic, 55 (3). pp. 333-348.

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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.

Item Type: Article
Uncontrolled Keywords: bmm∗,a−bmm∗,++,honestly consistent statement,pmax
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 11 Oct 2016 09:00
Last Modified: 24 Jul 2019 19:03
URI: https://ueaeprints.uea.ac.uk/id/eprint/60831
DOI: 10.1215/00294527-2688051

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