  Game semantics allows us to look at basic logical concepts from another side.
This approach to logic has a long history, there are plenty of different types
of games: provability games, semantic games, etc. And there is an interesting
type of provability games called Mezhirov's game proposed by Iliya Mezhirov for
intuitionistic logic of propositions and Grzegorczyk modal logic. Mezhirov's
game semantics for intuitionistic logic is interesting because of its
simplicity and strong connection with Kripke semantics and Kripke models. In my
study, I try to generalize Mezhirov's result in two directions: to generalize
to intuitionistic logic of predicates (or to some its extensions) and to the
case of a connection not only between the game and tautologies of logic, but
also between the game and entailment from infinite sets of formulas.
