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arXiv · 2303.05198

Infinitely many absolute universes

U. Larsson·R. J. Nowakowski·C. P. Santos
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Abstract

Absolute combinatorial game theory was recently developed as a unifying tool for constructive/local game comparison (Larsson et al. 2018). The theory concerns {\em parental universes} of combinatorial games; standard closure properties are satisfied and each pair of non-empty sets of forms of the universe makes a form of the universe. Here we prove that there is an infinite number of absolute mis\`ere universes, by recursively expanding the dicot mis\`ere universe and the dead-ending universe. On the other hand, we prove that normal-play has exactly two absolute universes, namely the full space, and the universe of all-small games.

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U. Larsson, R. J. Nowakowski, C. P. Santos. 2023-03-09. Infinitely many absolute universes. https://arxiv.org/abs/2303.05198

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