7 problems

In infinite chess, a position has a game value given by the ordinal rank measuring how many moves a player can force before winning, when such a value is defined. Evans–Hamkins con…

Evans–Hamkins conjecture. The upper bounds

For infinite chess, let $\omega_1^{\mathfrak{Ch}}$ be the supremum of game values for positions with at most finitely many pieces, let $\omega_1^{{\mathfrak{Ch}},c}$ and…

Let $\omega_1^{\widetilde{\mathfrak{Ch}}}$ denote the supremum of game values arising from arbitrary positions of infinite chess, including positions with infinitely many pieces. T…

In infinite chess, the omega one of chess is the supremum of the ordinal game values of positions; the lightface value $\omega_1^{\mathfrak{Ch}}$ takes the supremum over positions…

In infinite chess, a finite position is a winning position for a designated player if that player has a strategy forcing a win, with no requirement that the win occur within any fi…

Let infinite chess be played on the board ${\mathbb Z}\times{\mathbb Z}$ with finitely many pieces in a position. For a fixed natural number $n$, the mate-in-$n$ problem asks wheth…