We develop duality between nuclei on Heyting algebras and certain binary relations on Heyting spaces. We show that those binary relations are in 1-1 correspondence with subframes of Heyting spaces. We introduce the notions of nuclear and dense nuclear varieties of Heyting algebras, and prove that a variety of Heyting algebras is nuclear iff it is a subframe variety, and that it is dense nuclear iff it is a cofinal subframe variety. We give an alternative proof that every (cofinal) subframe variety of Heyting algebras is generated by its finite members.

An Algebraic Approach to Subframe Logics. Intuitionistic Case / G. Bezhanishvili, S. Ghilardi. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - 147:1-2(2007 Jun), pp. 84-100. [10.1016/j.apal.2007.04.001]

An Algebraic Approach to Subframe Logics. Intuitionistic Case

S. Ghilardi
Ultimo
2007

Abstract

We develop duality between nuclei on Heyting algebras and certain binary relations on Heyting spaces. We show that those binary relations are in 1-1 correspondence with subframes of Heyting spaces. We introduce the notions of nuclear and dense nuclear varieties of Heyting algebras, and prove that a variety of Heyting algebras is nuclear iff it is a subframe variety, and that it is dense nuclear iff it is a cofinal subframe variety. We give an alternative proof that every (cofinal) subframe variety of Heyting algebras is generated by its finite members.
Heyting algebras; Local operators; Nuclei; Subframe logics
Settore M-FIL/02 - Logica e Filosofia della Scienza
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/35562
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