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Propositional quantification in the monadic fragment of intuitionistic logic

Published online by Cambridge University Press:  12 March 2014

Tomasz Połacik
Tomasz Połacik*
Affiliation:
Institute of Mathematics, University of Silesia, Katowice, Poland, E-mail: polacik@us.edu.pl
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Abstract

We study the monadic fragment of second order intuitionistic propositional logic in the language containing the standard propositional connectives and propositional quantifiers. It is proved that under the topological interpretation over any dense-in-itself metric space, the considered fragment collapses to Heyting calculus. Moreover, we prove that the topological interpretation over any dense-in-itself metric space of fragment in question coincides with the so-called Pitts' interpretation. We also prove that all the nonstandard propositional operators of the form q ↦ ∃p (q ↔ F(p)), where F is an arbitrary monadic formula of the variable p, are definable in the language of Heyting calculus under the topological interpretation of intuitionistic logic over sufficiently regular spaces.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 1 , March 1998 , pp. 269 - 300
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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