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A temporal-theoretic formalism for understanding game theory is describedwhere a strict ordering relation on a set of time points $T$ defines a game on$T$. Using this formalism, a proof of Zermelo's Theorem, which states thatevery finite 2-player zero-sum game is determined, is given and an exhaustiveanalysis of the game of Nim is presented. Furthermore, a combinatorial analysisof games on a set of arbitrary time points is given; in particular, it isproved that the number of distinct games on a set $T$ with cardinality $n$ isthe number of partial orders on a set of $n$ elements. By generalizing thistheorem from temporal modal frames to S5 modal frames, it is proved that thenumber of isomorphism classes of S5 modal frames $\mathcal{F} = \ < W, R \ >$with $|W|=n$ is equal to the partition function $p(n)$. As a corollary of thefact that the partition function is asymptotic to the Hardy-Ramanujan number$$\frac{1}{4\sqrt{3}n}e^{\pi \sqrt{2n/3}}$$ the number of isomorphism classesof S5 modal frames $\mathcal{F} = \ < W, R \ >$ with $|W|=n$ is asymptoticallythe Hardy-Ramanujan number. Lastly, we use these results to prove that anarbitrary modal frame is an S5 modal frame with probability zero.

On Generalizing a Temporal Formalism for Game Theory to the Asymptotic Combinatorics of S5 Modal Frames