 Tarski’s approach fails because the string of quantifiers at the beginning is infinite, and we would never reach an end of stripping them off. Instead, Henkin suggested, we should consider the game where a person \(\forall\) chooses an object \(a_0\) for \(x_0\), then a second person \(\exists\) chooses an object \(b_0\) for \(y_0\), then \(\forall\) chooses \(a_1\) for \(x_1, \exists\) chooses \(b_1\) for \(y_1\) and so on. A play of this game is a win for \(\exists\) if and only if the infinite atomic sentence