Notre Dame Journal of Formal Logic

Intuitionistic Completeness and Classical Logic

D. C. McCarty

Abstract

We show that, if a suitable intuitionistic metatheory proves that consistency implies satisfiability for subfinite sets of propositional formulas relative either to standard structures or to Kripke models, then that metatheory also proves every negative instance of every classical propositional tautology. Since reasonable intuitionistic set theories such as HAS or IZF do not demonstrate all such negative instances, these theories cannot prove completeness for intuitionistic propositional logic in the present sense.

Article information

Source
Notre Dame J. Formal Logic, Volume 43, Number 4 (2002), 243-248.

Dates
First available in Project Euclid: 17 January 2004

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1074396309

Digital Object Identifier
doi:10.1305/ndjfl/1074396309

Mathematical Reviews number (MathSciNet)
MR2034749

Zentralblatt MATH identifier
1050.03041

Subjects
Primary: 03F55: Intuitionistic mathematics 03F50: Metamathematics of constructive systems

Keywords
intuitionistic logic completeness incompleteness

Citation

McCarty, D. C. Intuitionistic Completeness and Classical Logic. Notre Dame J. Formal Logic 43 (2002), no. 4, 243--248. doi:10.1305/ndjfl/1074396309. https://projecteuclid.org/euclid.ndjfl/1074396309


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References

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