David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Studia Logica 49 (1):133 - 149 (1990)
Let g E(m, n)=o mean that n is the Gödel-number of the shortest derivation from E of an equation of the form (m)=k. Hao Wang suggests that the condition for general recursiveness mn(g E(m, n)=o) can be proved constructively if one can find a speedfunction s s, with s(m) bounding the number of steps for getting a value of (m), such that mn s(m) s.t. g E(m, n)=o. This idea, he thinks, yields a constructivist notion of an effectively computable function, one that doesn't get us into a vicious circle since we intuitively know, to begin with, that certain proofs are constructive and certain functions effectively computable. This paper gives a broad possibility proof for the existence of such classes of effectively computable functions, with Wang's idea of effective computability generalized along a number of dimensions.
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References found in this work BETA
Hao Wang (1966). A Survey of Mathematical Logic. Philosophical Review 75 (2):240-244.
Hartley Rogers (1965). Review: A. A. Mucnik, Solution of Post's Reduction Problem and of Certain Other Problems in the Theory of Algorithms. I. [REVIEW] Journal of Symbolic Logic 30 (1):90-90.
Citations of this work BETA
F. W. Kroon (1996). The Intrinsic Difficulty of Recursive Functions. Studia Logica 56 (3):427 - 454.
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