Varieties of monadic Heyting algebras part II: Duality theory

Studia Logica 62 (1):21-48 (1999)
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Abstract

In this paper we continue the investigation of monadic Heyting algebras which we started in [2]. Here we present the representation theorem for monadic Heyting algebras and develop the duality theory for them. As a result we obtain an adequate topological semantics for intuitionistic modal logics over MIPC along with a Kripke-type semantics for them. It is also shown the importance and the effectiveness of the duality theory for further investigation of monadic Heyting algebras and logics over MIPC.

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2004

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10.1023/a:1005173628262

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References found in this work

Heyting Algebras: Duality Theory.Leo Esakia - 2019 - Cham, Switzerland: Springer Verlag.
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
Topoi: The Categorial Analysis of Logic.R. I. Goldblatt - 1982 - British Journal for the Philosophy of Science 33 (1):95-97.
On Closed Elements in Closure Algebras.J. C. C. Mckinsey & Alfred Tarski - 1946 - Annals of Mathematics, Ser. 2 47:122-162.

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