**November 17**

**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).