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On the strong semantical completeness of the intuitionistic predicate calculus

Published online by Cambridge University Press:  12 March 2014

Richmond H. Thomason
Richmond H. Thomason*
Affiliation:
Yale University
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Extract

In Kripke [8] the first-order intuitionjstic predicate calculus (without identity) is proved semantically complete with respect to a certain model theory, in the sense that every formula of this calculus is shown to be provable if and only if it is valid. Metatheorems of this sort are frequently called weak completeness theorems—the object of the present paper is to extend Kripke's result to obtain a strong completeness theorem for the intuitionistic predicate calculus of first order; i.e., we will show that a formula A of this calculus can be deduced from a set Γ of formulas if and only if Γ implies A. In notes 3 and 5, below, we will indicate how to account for identity, as well. Our proof of the completeness theorem employs techniques adapted from Henkin [6], and makes no use of semantic tableaux; this proof will also yield a Löwenheim-Skolem theorem for the modeling.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 1 , 26 April 1968 , pp. 1 - 7
Copyright
Copyright © Association for Symbolic Logic 1968

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References

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