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An embedding of classical logic in S4

Published online by Cambridge University Press:  12 March 2014

Melvin Fitting
Melvin Fitting*
Affiliation:
Lehman College, Cuny, New York, New York10468
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Extract

There are well-known embeddings of intuitionistic logic into S4 and of classical logic into S5. In this paper we give a related embedding of (first order) classical logic directly into (first order) S4, with or without the Barcan formula. If one reads the necessity operator of S4 as ‘provable’, the translation may be roughly stated as: truth may be replaced by provable consistency. A proper statement will be found below. The proof is based ultimately on the notion of complete sequences used in Cohen's technique of forcing [1], and is given in terms of Kripke's model theory [3], [4].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 4 , December 1970 , pp. 529 - 534
Copyright
Copyright © Association for Symbolic Logic 1971

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References

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