Fragments of Martin's Maximum in generic extensions

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Mathematical Logic Quarterly 50 (3):297 (2004)
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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-closed

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10.1002/malq.200410101

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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.
Forcing axioms, approachability, and stationary set reflection.Sean D. Cox - 2021 - Journal of Symbolic Logic 86 (2):499-530.
Kurepa trees and Namba forcing.Bernhard König & Yasuo Yoshinobu - 2012 - Journal of Symbolic Logic 77 (4):1281-1290.

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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.
Scales, squares and reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
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.

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