Journal of Symbolic Logic 72 (1):349 - 360 (2007)
Abstract |
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Lévy collapse. These show in particular that certain applications of forcing axioms require to add generic countable sequences high up in the set-theoretic hierarchy even before collapsing everything down to א₁. Later we give applications, among them the consistency of MM with אω not being Jónsson which answers a question raised in the set theory meeting at Oberwolfach in 2005
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DOI | 10.2178/jsl/1174668399 |
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References found in this work BETA
The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal.W. Hugh Woodin - 2002 - Bulletin of Symbolic Logic 8 (1):91-93.
Bounded Forcing Axioms as Principles of Generic Absoluteness.Joan Bagaria - 2000 - Archive for Mathematical Logic 39 (6):393-401.
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Citations of this work BETA
The Combinatorial Essence of Supercompactness.Christoph Weiß - 2012 - Annals of Pure and Applied Logic 163 (11):1710-1717.
Guessing Models and the Approachability Ideal.Rahman Mohammadpour & Boban Veličković - 2020 - Journal of Mathematical Logic 21 (2):2150003.
Forcing Axioms, Supercompact Cardinals, Singular Cardinal Combinatorics.Matteo Viale - 2008 - Bulletin of Symbolic Logic 14 (1):99-113.
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