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Approachability and Games on Posets

  • Yasuo Yoshinobu (a1)

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 [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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