1. Infinitely many absolute universes
- Author
-
Larsson, U., Nowakowski, R. J., and Santos, C. P.
- Subjects
Mathematics - Combinatorics ,Computer Science - Discrete Mathematics ,91A46 - 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., Comment: 19 pages
- Published
- 2023