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A model theoretic characterization of effective operations

  • M. H. Löb (a1)
  • Please note a correction has been issued for this article.

Extract

Let be a standard formalization of type theory. In [6] Kreisel introduced N-models for . These are general models in the sense of [1] in which the numerals have their standard denotations.

If ξ is a closed term of we shall denote the object denoted by ξ in the N-model M by ξM. In particular, ξ* is the object denoted by ξ in the standard model of .

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[1]Henkin, L., The completeness in the theory of types, this Journal, vol. 15 (1950), pp. 8191.
[2]Kleene, S. C., Introduction to metamathematics, North-Holland, Amsterdam, 1964.
[3]Kleene, S. C., Countable functionals, Constructivity in mathematics, edited by Heyting, A., North-Holland, Amsterdam, 1959, pp. 81100.
[4]Kreisel, G., Interpretation of analysis by means of functionals of finite types, Constructivity in mathematics, North-Holland, Amsterdam, 1959, pp. 101128.
[5]Kreisel, G., Lacombe, D. and Schoenfield, J. R., Partial recursive functionals and effective operations, Constructivity in mathematics, North-Holland, Amsterdam, 1959, pp. 290297.
[6]Kreisel, G., Set-theoretic problems suggested by the notions of potential totality, Infinitistic methods, Warsaw, Poland, 1959, pp. 103140.
[7]Kreisel, G., Lacombe, D. and Schoenfield, J. R., Fonctionelles recursivement définissables et fonctionelles récursives, Comptes rendus, vol. 245 (1959), pp. 399–342.
[8]Myhill, J. R. and Shepherdson, J. C., Effective operations and partial recursive functions, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 1 (1955), pp. 310317.
[9]Tarski, A., Der Wahrheitsbegriff in den formalisierten Sprachen, Studia philosophica, vol. 1 (1936), pp. 261405.

A model theoretic characterization of effective operations

  • M. H. Löb (a1)
  • Please note a correction has been issued for this article.

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A correction has been issued for this article: