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Are mathematical game-formalism and set theoretical foundations of mathematics (ZFC, for example) compatible? If not, where to start with a mathematical game-formalism foundations on their own? Are there any books on this matter?

REMARK: I am not talking about game theory, I am talking about the term this article is referring to.

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  • $\begingroup$ Firstly, I don't know a thing about the subject matter. But, according to Game semantics at Wikipedia: 'Assuming the axiom of choice, the game-theoretical semantics for classical first-order logic agree with the usual model-based (Tarskian) semantics.' So it sounds like they coexist peacefully, at least for first-order logic. $\endgroup$ Commented Jul 21, 2013 at 16:51
  • $\begingroup$ Please, check the remark I've added to the main post. $\endgroup$ Commented Jul 21, 2013 at 17:59
  • $\begingroup$ @Constatine, I've taken a good look at that article and its rather involved, so I don't think I can be of much help. Anyway, good luck. I've got your question favorited so I'll be interested to see whether anything pops up. $\endgroup$ Commented Jul 21, 2013 at 18:06

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There are many mathematical game formalisms. I guess you might be thinking of Conway's formalism of combinatorial, zero-sum, two-player games. But there are also games with numerical payoffs, games with more than two players, non-zero sum games, games involving randomness, games with infinite (and even transfinite) sequences of moves, and probably others that I'm not thinking of right now. All of these have mathematical theories, and all are "compatible with ZFC" in the sense of being formalizable in ZFC (just as almost all of the rest of mathematics is).

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