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- W2017254147 abstract "Abstract We show that the existence of a recursively enumerable set whose Turing degree is neither low nor complete cannot be proven from the basic axioms of first order arithmetic ( P − ) together with Σ 2 -collection ( B Σ 2 ). In contrast, a high (hence, not low) incomplete recursively enumerable set can be assembled by a standard application of the infinite injury priority method. Similarly, for each n , the existence of an incomplete recursively enumerable set that is neither low n nor high n -1 , while true, cannot be established in P − + BΣ n+1 . Consequently, no bounded fragment of first order arithmetic establishes the facts that the high n and low n jump hierarchies are proper on the recursively enumerable degrees." @default.
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- W2017254147 modified "2023-10-18" @default.
- W2017254147 title "Σ2-collection and the infinite injury priority method" @default.
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- W2017254147 doi "https://doi.org/10.1017/s0022481200029042" @default.
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