 On the other hand, quantifier independence is implemented at the level of strategies. Consequently independence indications following a universal quantifier are vacuous, when the satisfaction of a formula (truth of a sentence) is considered. Similarly, independence indications following an existential quantifier are vacuous when the dissatisfaction of a formula (falsity of a sentence) is at stake. The sentence \(\phi\) is true in the model \(M\) iff player 2 has a winning strategy \(F=\{c\}\) in game \(G(\phi , M)\). This, again, means that whichever elements \(a\) and \(b\) player 1 chooses to interpret \((\forall x)\) and \((\forall z/\exists y)\), respectively, the constant interpretation \(c\) of \((\exists y/\forall x)\) given by the (zero-place) strategy function \(c\) satisfies \(R(a, c, b)\) in \(M\). But this amounts to the same as requiring that whichever elements \(a\) and \(b\) player 1 chooses to interpret \((\forall x)\) and \((\forall z)\), respectively, the constant interpretation \(c\) of \((\exists y/\forall x)\) satisfies \(R(a, c, b)\) in \(M\). Indeed, \(\phi\) is truth equivalent to a sentence containing no slashed universal quantifiers: 