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The decidability of the Kreisel-Putnam system1

Published online by Cambridge University Press:  12 March 2014

Dov M. Gabbay
Dov M. Gabbay*
Affiliation:
Hebrew University of Jerusalem
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Extract

The intuitionistic propositional logic I has the following disjunction property

This property does not characterize intuitionistic logic. For example Kreisel and Putnam [5] showed that the extension of I with the axiom

has the disjunction property. Another known system with this propery is due to Scott [5], and is obtained by adding to I the following axiom:

In the present paper we shall prove, using methods originally introduced by Segerberg [10], that the Kreisel-Putnam logic is decidable. In fact we shall show that it has the finite model property, and since it is finitely axiomatizable, it is decidable by [4]. The decidability of Scott's system was proved by J. G. Anderson in his thesis in 1966.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 3 , September 1970 , pp. 431 - 437
Copyright
Copyright © Association for Symbolic Logic 1971

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Footnotes

1

This research was sponsored under contract no. N00014–69-G-0192 U.S. Office of Naval Research, Information System Branch.

References

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