Formulas of one propositional variable in intuitionistic logic with the Solovay modality

Leo Esakia, Revaz Grigolia

DOI: http://dx.doi.org/10.12775/LLP.2008.007

Abstract


A description of the free cyclic algebra over the variety of Solovay algebras, as well as over its pyramid locally finite subvarieties is given.

Keywords


Heyting algebras; Kripke frames; free algebras

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References


Abashidze, M., “On some properties of Magari algebras”, pages 111–127 in Logical-Semantical Investigations, Tbilisi, Metsniereba, 1981 (in Russian).

Boolos, G., The Logic of Provability, Cambridge Univ. Press, 1993, XV, 276.

Esakia, L., Heyting Algebras I. Duality Theory, Monograph, “Metsniereba”, Tbilisi, 1985 (in Russian).

Esakia, L.,“Provability interpretation of Intuitionistic Logic”, pages 19–24 in Logical Investigations 5, Moscow, Nauka, 1998 (in Russian).

Esakia, L., and R. Grigolia, “The criterion of Browerian and closure algebras to be finiteliy generated”, Bull. Sect. Logic 6, 2 (1973), 46–52.

Grigolia, R., Free Algebras of Non Classical Logics, Monograph, “Metsniereba”, Tbilisi, 1987 (in Russian).

Kuznetsov, A., and A. Muravitsky, “On superintuitionistic logics as fragments of proof logic extensions”, Studia Logica 45 (1986), 77–99.

Solovay, R., ‘Provability interpretation of modal logics’, Israel Journal of Mathematics 25 (1976), 287–304.








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ISSN: 1425-3305 (print version)
ISSN: 2300-9802 (electronic version)

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