Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T19:26:38.045Z Has data issue: false hasContentIssue false

A model theoretic characterization of effective operations

Published online by Cambridge University Press:  12 March 2014

M. H. Löb*
Affiliation:
University of Leeds

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 .

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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