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- W2964177411 abstract "Abstract We prove that the statement “there is a k such that for every f there is a k -bounded diagonally nonrecursive function relative to f ” does not imply weak König’s lemma over ${rm{RC}}{{rm{A}}_0} + {rm{BSigma }}_2^0$ . This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every k -bounded diagonally nonrecursive function computes a 2-bounded diagonally nonrecursive function may fail in the absence of ${rm{ISigma }}_2^0$ ." @default.
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- W2964177411 date "2015-12-01" @default.
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- W2964177411 title "COMPARING THE STRENGTH OF DIAGONALLY NONRECURSIVE FUNCTIONS IN THE ABSENCE OF INDUCTION" @default.
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- W2964177411 doi "https://doi.org/10.1017/jsl.2015.43" @default.
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