 is true. The original sentence is true if and only if player \(\exists\) has a winning strategy for this game. Strictly Henkin used the game only as a metaphor, and the truth condition that he proposed was that the skolemised version of the sentence is true, i.e. that there are functions \(f_0, f_1,\ldots\) such that for every choice of \(a_0, a_1, a_2\) etc. we have