with it, if certain large cardinals are consistent.

Background

Gale–Stewart games

A Gale–Stewart game is a two-player game of perfect information. The game is defined using a set A, and is denoted G_A. The two players alternate turns, and each player is aware of all moves before making the next one. On each turn, each player chooses a single element of A to play. The same element may be chosen more than once without restriction. The game can be

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