Abstract
We show that for any infinite cardinal κ, every strongly (κ+1)-strategically closed poset is strongly κ+-strategically closed if and only if APκ (the approachability property) holds, answering the question asked in [k5]. We also give a complete classification of strengths of strategic closure properties and that of strong strategic closure properties respectively.
Citation
Yasuo Yoshinobu. "Approachability and games on posets." J. Symbolic Logic 68 (2) 589 - 606, June 2003. https://doi.org/10.2178/jsl/1052669065
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