Stochastic Games. I. Foundations,

This paper strives to provide a sound underpinning for the theory of stochastic games. Section 2 is a reworking of the Bewley-Kohlberg result integrated with Shapleys the black magic of Tarskis principle is replaced by the gray magic of the Hilbert Nullstellensatz. Section 3 explicates the underlying topology and measure theory I believe it is as necessary for Mertens and Neymans proof of the minmax theorem as it is for mine. Finally, Section 4 establishes a result on this sort of structure which may be of some independent interest.