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Definability theorem for the intuitionistic predicate logic with equality

Published online by Cambridge University Press:  22 January 2016

Chiharu Mizutani
Chiharu Mizutani*
Affiliation:
Department of Mathematics, University of Tsukuba, Sakuramura Ibaraki, 300-31, Japan
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Svenonius’ definability theorem and its generalizations to the infinitary logic Lω1ω or to a second order logic with countable conjunctions and disjunctions have been studied by Kochen [1], Motohashi [2], [3] or Harnik and Makkai [4], independently. In this paper, we consider a (Svenonius-type) definability theorem for the intuitionistic predicate logic IL with equality.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 87 , November 1982 , pp. 1 - 15
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[1] Kochen, S., Topics in the theory of definition, Proc. of Model Theory Symposium, Berkeley, 1963 (1965), 170–176.Google Scholar
[2] Motohashi, N., Interpolation theorem and characterization theorem, Ann. Japan Assoc. Philos. Soc, 4 (1972), 85–150.Google Scholar
[3] Motohashi, N., A new theorem on definability in a positive second order logic with countable conjunctions and disjunctions, Proc. Japan Acad., 48 (1972), 153–156.Google Scholar
[4] Harnik, V. and Makkai, M., Application of Vaught sentences and the covering theorem, J.S.L., 41, 1 (1976), 171–187.Google Scholar
[5] Troelstra, A. S., Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, Lecture Notes in Mathematics, 344, Springer-Verlag, (1973).Google Scholar