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Tarski's Fixpoint Lemma and combinatorial games

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Abstracts

Using Tarski's Fixpoint Lemma for order preserving maps of a complete lattice into itself, a new, lattice theoretic proof is given for the existence of persistent strategies for combinatorial games as well as for games with a topological tolerance and games on lattices. Further, the existence of winning strategies is obtained for games on superalgebraic lattices, which includes the case of ordinary combinatorial games. Finally, a basic representation theorem is presented for those lattices.

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Communicated by D. Duffus

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Banaschewski, B., Pultr, A. Tarski's Fixpoint Lemma and combinatorial games. Order 7, 375–386 (1990). https://doi.org/10.1007/BF00383202

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AMS subject classifications (1980)

  • 90D05
  • 90D42
  • 06A99

Key words

  • combinatorial games
  • Tarski's Fixpoint Lemma
  • persistent strategies
  • winning strategies
  • superalgebraic lattices