Approachability and games on posets

Journal of Symbolic Logic 68 (2):589-606 (2003)
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Abstract

We show that for any infinite cardinal κ, every strongly $(\kappa + 1)-strategically$ closed poset is strongly $\kappa^+-strategically$ closed if and only if $AP_\kappa$ (the approachability property) holds, answering the question asked in [5]. We also give a complete classification of strengths of strategic closure properties and that of strong strategic closure properties respectively

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10.2178/jsl/1052669065

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Citations of this work

Fragments of Martin's Maximum in generic extensions.Y. Yoshinobu & B. Konig - 2004 - Mathematical Logic Quarterly 50 (3):297.
Forcing Indestructibility of Set-Theoretic Axioms.Bernhard König - 2007 - Journal of Symbolic Logic 72 (1):349 - 360.
Operations, climbability and the proper forcing axiom.Yasuo Yoshinobu - 2013 - Annals of Pure and Applied Logic 164 (7-8):749-762.
Destructibility of stationary subsets of Pκλ.Sakaé Fuchino & Greg Piper - 2005 - Mathematical Logic Quarterly 51 (6):560-569.

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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.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

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