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Fragments of Martin's Maximum in generic extensions
Mathematical Logic Quarterly 50 (3):297 (2004)
Abstract
We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly -game-closed forcings. PFA can be destroyed by a strongly -game-closed forcing but not by an ω2-closedOther Versions
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Citations of this work
Fragility and indestructibility of the tree property.Spencer Unger - 2012 - Archive for Mathematical Logic 51 (5-6):635-645.
The Proper Forcing Axiom and the Singular Cardinal Hypothesis.Matteo Viale - 2006 - Journal of Symbolic Logic 71 (2):473 - 479.
Kurepa trees and Namba forcing.Bernhard König & Yasuo Yoshinobu - 2012 - Journal of Symbolic Logic 77 (4):1281-1290.
Forcing axioms, approachability, and stationary set reflection.Sean D. Cox - 2021 - Journal of Symbolic Logic 86 (2):499-530.
Dependent choice, properness, and generic absoluteness.David Asperó & Asaf Karagila - forthcoming - Review of Symbolic Logic:1-25.
References found in this work
Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Aronszajn trees and the independence of the transfer property.William Mitchell - 1972 - Annals of Mathematical Logic 5 (1):21.
Separating stationary reflection principles.Paul Larson - 2000 - Journal of Symbolic Logic 65 (1):247-258.
Semiproper forcing axiom implies Martin maximum but not PFA+.Saharon Shelah - 1987 - Journal of Symbolic Logic 52 (2):360-367.
Approachability and games on posets.Yasuo Yoshinobu - 2003 - Journal of Symbolic Logic 68 (2):589-606.
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