Open Access
2014 Bounded Martin’s Maximum with an Asterisk
David Asperó, Ralf Schindler
Notre Dame J. Formal Logic 55(3): 333-348 (2014). DOI: 10.1215/00294527-2688051


We isolate natural strengthenings of Bounded Martin’s Maximum which we call BMM and ABMM,++ (where A is a universally Baire set of reals), and we investigate their consequences. We also show that if ABMM,++ holds true for every set of reals A in L(R), then Woodin’s axiom () holds true. We conjecture that MM++ implies ABMM,++ for every A which is universally Baire.


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


Published: 2014
First available in Project Euclid: 22 July 2014

zbMATH: 1338.03101
MathSciNet: MR3263531
Digital Object Identifier: 10.1215/00294527-2688051

Primary: 03E55 , 03E57
Secondary: 03E35 , 03E60

Keywords: $\mathbb{P}_{\mathrm{max}}$ , ${\mathsf{BMM}}^{*}$ , $A-{\mathsf{BMM}}^{*,++}$ , honestly consistent statement

Rights: Copyright © 2014 University of Notre Dame

Vol.55 • No. 3 • 2014
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