Ehrenfeucht–Fraïssé game

The Ehrenfeucht–Fraïssé (EF) game is a game-theoretic method used in model theory, a branch of mathematical logic. It serves as a tool for comparing structures in terms of their properties and behaviors. The game helps establish whether two mathematical structures (often models of a particular language or theory) satisfy the same first-order properties, which is important for understanding their equivalence in a logical sense. ### Structure of the Game 1.