Journal of Symbolic Logic

Woodin's axiom (*), bounded forcing axioms, and precipitous ideals on ω₁

Benjamin Claverie and Ralf Schindler

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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].

Article information

Source
J. Symbolic Logic, Volume 77, Issue 2 (2012), 475-498.

Dates
First available in Project Euclid: 4 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1333566633

Digital Object Identifier
doi:10.2178/jsl/1333566633

Mathematical Reviews number (MathSciNet)
MR2963017

Zentralblatt MATH identifier
1250.03111

Citation

Claverie, Benjamin; Schindler, Ralf. Woodin's axiom (*), bounded forcing axioms, and precipitous ideals on ω₁. J. Symbolic Logic 77 (2012), no. 2, 475--498. doi:10.2178/jsl/1333566633. https://projecteuclid.org/euclid.jsl/1333566633


Export citation