caa a22 4500 465779220 CHVBK 20180323111950.0 cr unu---uuuuu 170327e19900301xx s 000 0 eng 10.1007/BF00401559 doi (NATIONALLICENCE)springer-10.1007/BF00401559 On a complexity-based way of constructivizing the recursive functions [Elektronische Daten] [F. Kroon, W. Burkhard] 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 ϕ(m)=k. Hao Wang suggests that the condition for general recursiveness ∀m∃n(g E(m, n)=o) can be proved constructively if one can find a speedfunction ϕ s s, with ϕ s(m) bounding the number of steps for getting a value of ϕ(m), such that ∀m∃n≦ϕ 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. Kluwer Academic Publishers, 1990 Kroon F. Department of Philosophy, The University of Auckland, Newzealand aut Burkhard W. Department of Philosophy, The University of Auckland, Newzealand aut Studia Logica Kluwer Academic Publishers 49/1(1990-03-01), 133-149 0039-3215 49:1<133 1990 49 11225 https://doi.org/10.1007/BF00401559 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00401559 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kroon F. Department of Philosophy, The University of Auckland, Newzealand aut NATIONALLICENCE 700 1- Burkhard W. Department of Philosophy, The University of Auckland, Newzealand aut NATIONALLICENCE 773 0- Studia Logica Kluwer Academic Publishers 49/1(1990-03-01), 133-149 0039-3215 49:1<133 1990 49 11225 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer