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Some results for implicational calculi

Published online by Cambridge University Press:  12 March 2014

R. A. Bull
R. A. Bull*
Affiliation:
Wadham College, Oxford
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Extract

I shall refer to the implicational fragment of intuitionist logic, and its extension with the further axiom

CCCCpqqrCCCpqrr

as IIC and OIC, respectively. The purpose of this paper is to apply a result due to Garrett Birkhoff to the extensions of IIC, and to the extensions of OIC in particular. The main result obtained is that every extension of OIC is characterised by finite models.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 29 , Issue 1 , March 1964 , pp. 33 - 39
Copyright
Copyright © Association for Symbolic Logic 1964

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References

[1]Birkhoff, Garrett, Subdirect unions in universal algebras. Bull. Am. Math. Soc., vol. 50 (1944), pp. 764–768.CrossRefGoogle Scholar
[2]Birkhoff, Garrett, Lattice Theory. American Mathematical Colloquium Publications, vol. XXV, New York, 1948.Google Scholar
[3]Harrop, R., On the existence of finite models and decision procedures for prepositional calculi. Proc. Camb. Phil. Soc., vol. 54 (1958), pp. 1–13.CrossRefGoogle Scholar
[4]Bull, R. A., The implicational fragment of Dummett's LC. This Journal, vol. 27 (1962), pp. 189–194.Google Scholar
[5]Thomas, Ivo, Finite limitations on Dummett's LC. Notre Dame Journal of Formal Logic, vol. III (1962), pp. 170–174.Google Scholar