Journal of Symbolic Logic 77 (2):475-498 (2012)

Abstract
If the Bounded Proper Forcing Axiom BPFA holds, then Mouse Reflection holds at N₂ with respect to all mouse operators up to the level of Woodin cardinals in the next ZFC-model. This yields that if Woodin's ℙ max 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 "NS ω1 is precipitous" and strengthenings thereof. Along the way, we answer a question of Baumgartner and Taylor. [2, Question 6.11]
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DOI 10.2178/jsl/1333566633
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References found in this work BETA

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
Combinatorial Principles in the Core Model for One Woodin Cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
Bounded Forcing Axioms as Principles of Generic Absoluteness.Joan Bagaria - 2000 - Archive for Mathematical Logic 39 (6):393-401.
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Square in Core Models.Ernest Schimmerling & Martin Zeman - 2001 - Bulletin of Symbolic Logic 7 (3):305-314.

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Citations of this work BETA

Virtual Large Cardinals.Victoria Gitman & Ralf Schindler - 2018 - Annals of Pure and Applied Logic 169 (12):1317-1334.
Diagonal Reflections on Squares.Gunter Fuchs - 2019 - Archive for Mathematical Logic 58 (1-2):1-26.
On a Class of Maximality Principles.Daisuke Ikegami & Nam Trang - 2018 - Archive for Mathematical Logic 57 (5-6):713-725.
In Memoriam: James Earl Baumgartner.J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7-8):877-909.
Bounded Martin’s Maximum with an Asterisk.David Asperó & Ralf Schindler - 2014 - Notre Dame Journal of Formal Logic 55 (3):333-348.

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