On the Difficulty of Writing Out formal Proofs in Arithmetic

Mathematical Logic Quarterly 43 (3):328-332 (1997)

Abstract
Let ℸ be the set of Gödel numbers Gn of function symbols f such that PRA ⊢ and let γ be the function such that equation imageWe prove: The r. e. set ℸ is m-complete; the function γ is not primitive recursive in any class of functions {f1, f2, ⃛} so long as each fi has a recursive upper bound. This implies that γ is not primitive recursive in ℸ although it is recursive in ℸ
Keywords Formal proofs in arithmetic  m‐complete set  Gödel's incompleteness theorem
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DOI 10.1002/malq.19970430305
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References found in this work BETA

Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers.Piergiorgio Odifreddi - 1989 - Sole Distributors for the Usa and Canada, Elsevier Science Pub. Co..
Self-Reference and Modal Logic.George Boolos & C. Smorynski - 1988 - Journal of Symbolic Logic 53 (1):306.
Self-Reference and Modal Logic.[author unknown] - 1987 - Studia Logica 46 (4):395-398.

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