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- W2034304297 abstract "Abstract We give a new characterization of the hyperarithmetic sets: a set X of integers is recursive in e α if and only if there is a Turing machine which computes X and “halts” in less than or equal to the ordinal number ω α of steps. This result represents a generalization of the well-known “limit lemma” due to J. R. Shoenfield [Sho-1] and later independently by H. Putnam [Pu] and independently by E. M. Gold [Go]. As an application of this result, we give a recursion theoretic analysis of clopen determinacy: there is a correlation given between the height α of a well-founded tree corresponding to a clopen game A ⊆ ω ω and the Turing degree of a winning strategy ƒ for one of the players—roughly, ƒ can be chosen to be recursive in 0 α and this is the best possible (see §4 for precise results)." @default.
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- W2034304297 date "1986-06-01" @default.
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- W2034304297 title "A generalization of the limit lemma and clopen games" @default.
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- W2034304297 doi "https://doi.org/10.1017/s0022481200031145" @default.
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