### Equivalences and Congruences on Infinite Conway Games

Taking the view that infinite plays are , we study and . These admit a sharp presentation, where non-terminating games are seen as a and game contructors, such as , as . We have shown, in a previous paper, that Conway’s theory of terminating games can be rephrased naturally in terms of game . Namely, various conceptually independent notions of can be defined and shown to coincide on Conway’s terminating games. These are the equivalence...