We prove a forgetful determinacy theorem saying that, for a wide class of infinitary games, one of the players has a winning strategy that is virtually memoryless: the player has to remember only bounded many bits of information. We use forgetful determinacy to give a transparent proof of Rabin’s celebrated result that the monadic second-order theory of the infinite tree is decidable.<\/p>\n","protected":false},"excerpt":{"rendered":"
We prove a forgetful determinacy theorem saying that, for a wide class of infinitary games, one of the players has a winning strategy that is virtually memoryless: the player has to remember only bounded many bits of information. 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