Joel David Hamkins, Notre Dame University
The Wordle and Absurdle numbers
We consider the game of infinite Wordle as played on Baire space $\omega^\omega$. The codebreaker can win in finitely many moves against any countable dictionary $\Delta\subseteq\omega^\omega$, but not against the full dictionary of Baire space. The Wordle number is the size of the smallest dictionary admitting such a winning strategy for the codebreaker, the corresponding Wordle ideal is the ideal generated by these dictionaries, which under MA includes all dictionaries of size less than the continuum. The Absurdle number, meanwhile, is the size of the smallest dictionary admitting a winning strategy for the absurdist in the two-player variant, infinite Absurdle. In ZFC there are nondetermined Absurdle games, with neither player having a winning strategy, but if one drops the axiom of choice, then the principle of Absurdle determinacy has large cardinal consistency strength over ZF+DC. This is joint work with Ben De Bondt (Paris).