 Semantic games \(G(\phi , M)\) for first-order sentences \(\phi\) are two-player zero-sum games of perfect information, played on a given model \(M\). Let us call the two players simply player 1 and player  2.[11]  The games are most easily explained for sentences in prenex form. Universal quantifiers mark a move of player 1, while existential quantifiers prompt a move by player 2. In both cases, the relevant player must choose an individual from the domain \(\rM\) of  \(M\).[12]  If