## Journal of Symbolic Logic

### Propositional Quantification in the Monadic Fragment of Intuitionistic Logic

Tomasz Polacik

#### 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 $\mapsto \exists$p (q $\leftrightarrow$ 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.

#### Article information

Source
J. Symbolic Logic, Volume 63, Issue 1 (1998), 269-300.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745471

Mathematical Reviews number (MathSciNet)
MR1610423

Zentralblatt MATH identifier
0959.03005

JSTOR