 Theorem (assuming AC). (Hodges 1983: 94, Hintikka &amp; Kulas 1985: 6–7) Let \(\tau\) be any vocabulary, \(M\) any \(\tau\) structure, \(g\) any variable assignment and \(\phi\) any \(\mathbf{FO}[\tau]\) formula. Then \(M, g \vDash \phi\) holds in the standard sense iff there is a winning strategy for player 2 in game \(G(\phi , M,  g)\).[35] 