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June 2012 Woodin's axiom (*), bounded forcing axioms, and precipitous ideals on ω₁
Benjamin Claverie, Ralf Schindler
J. Symbolic Logic 77(2): 475-498 (June 2012). DOI: 10.2178/jsl/1333566633

Abstract

If the Bounded Proper Forcing Axiom BPFA holds, then Mouse Reflection holds at ℵ₂ with respect to all mouse operators up to the level of Woodin cardinals in the next ZFC—model. This yields that if Woodin's ℛmax axiom (*) holds, then BPFA implies that V is closed under the “Woodin-in-the-next-ZFC—model” operator. We also discuss stronger Mouse Reflection principles which we show to follow from strengthenings of BPFA, and we discuss the theory BPFA plus “NSω₁ is precipitous” and strengthenings thereof. Along the way, we answer a question of Baumgartner and Taylor, [2, Question 6.11].

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Benjamin Claverie. Ralf Schindler. "Woodin's axiom (*), bounded forcing axioms, and precipitous ideals on ω₁." J. Symbolic Logic 77 (2) 475 - 498, June 2012. https://doi.org/10.2178/jsl/1333566633

Information

Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1250.03111
MathSciNet: MR2963017
Digital Object Identifier: 10.2178/jsl/1333566633

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 2 • June 2012
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