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The class of surreal numbers (commonly called $No$) is not complete: it contains gaps. Some people have studied the "Dedekind completion" of the surreal numbers in order to do limits and ...

As follow up to Checkmate in $\omega$ moves?, we can ask the same question about go. Is there a position on a $\mathbb Z \times \mathbb Z$ goban such that either black can kill a white group, but ...

I am looking for references and hopefully enlightening proofs of the following statement(s) concerning the determinacy of not-necessarily-well-founded (i.e., possibly infinite, possibly loopy) ...

Is there a chess position with a finite number of pieces on the infinite chess board $\mathbb{Z}^2$ such that White to move has a forced win, but Black can stave off mate for at least $n$ moves for ...

The recent question Do there exist chess positions that require exponentially many moves to reach? of Tim Chow reminds me of a problem I have been interested in. Is chess with finitely many men on an ...