caa a22 4500 388039604 CHVBK 20180307125017.0 cr unu---uuuuu 161130e199803 xx s 000 0 eng 10.2307/2586601 doi S0022481200015462 pii (NATIONALLICENCE)cambridge-10.2307/2586601 Połacik Tomasz Institute of Mathematics, University of Silesia, Katowice, Poland, E-mail: polacik@us.edu.pl Propositional quantification in the monadic fragment of intuitionistic logic [Elektronische Daten] [Tomasz Połacik] 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. Copyright © Association for Symbolic Logic 1998 The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 269-300 0022-4812 63:1<269 1998 63 JSL https://doi.org/10.2307/2586601 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586601 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Połacik Tomasz Institute of Mathematics, University of Silesia, Katowice, Poland, E-mail: polacik@us.edu.pl NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 269-300 0022-4812 63:1<269 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge