Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T21:01:47.293Z Has data issue: false hasContentIssue false
  • English
  • Français

Implicit definability and infinitary languages1

Published online by Cambridge University Press:  12 March 2014

Kenneth Kunen
Kenneth Kunen*
Affiliation:
Stanford University
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper we define the notions of invariant implicit definability (i.i.d.) and semi-invariant implicit definability (s.i.i.d.) on ε-models, A, of a certain weak set theory. These notions are intended to be the analogs of recursiveness and recursive enumerability, respectively. Following Barwise, with each A is associated an infinitary language whose formulas are elements of A.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 3 , 10 October 1968 , pp. 446 - 451
Copyright
Copyright © Association for Symbolic Logic 1968

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.)

Footnotes

1

This work was supported by ε NSF Graduate Fellowship.

References

[1]Barwise, J., α-finlte derivations of α-finite theorems, abstract, this Journal, vol. 32 (1967), p. 431.Google Scholar
[2]Barwise, J., Doctoral dissertation, Stanford University, Stanford, Calif., 1967.Google Scholar
[3]Feferman, S. and Kreisel, G., Persistent and invariant formulas relative to theories of higher order, Bulletin of the American Mathematical Society, vol. 72 (1966), pp. 480–485.CrossRefGoogle Scholar
[4]Fra, R.ῑssé, Une notion de récursivité relative, Infinitistic methods, Proceedings of the symposia on foundations of mathematics, Warsaw, 1959, pp. 323–328.Google Scholar
[5]Hanf, W., Incompactness in languages with infinitely long expressions, Fundamenta mathematical, vol. 53 (1964), pp. 309–324.CrossRefGoogle Scholar
[6]Lévy, A., A hierarchy of formulas in set theory, Memoirs of the American Mathematical Society, no. 57 (1965).Google Scholar
[7]Karp, C., Languages with expressions of Infinite length, North-Holland, Amsterdam, 1964.Google Scholar
[8]Kreisel, G., Model-theoretic invariants: applications to recursive and hyperarithmetic operations, The theory of models, Proceedings of the 1963 International symposium at Berkeley, North-Holland, Amsterdam, 1965, pp. 190–205.Google Scholar
[9]Kripke, S., Transfinite recursions on admissible ordinals, abstracts, this Journal, vol. 29 (1964), pp. 161–162.Google Scholar