An algebraic approach to subframe logics. Intuitionistic case

Annals of Pure and Applied Logic 147 (1):84-100 (2007)
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Abstract

We develop duality between nuclei on Heyting algebras and certain binary relations on Heyting spaces. We show that these 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 subframe variety of Heyting algebras is generated by its finite members

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References found in this work

The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
Logics containing k4. part II.Kit Fine - 1985 - Journal of Symbolic Logic 50 (3):619-651.
Sur les Algèbres de Hilbert.Antonio Diego, Jean Porte & Luisa Iturrioz - 1970 - Journal of Symbolic Logic 35 (1):139-139.
The structure of lattices of subframe logics.Frank Wolter - 1997 - Annals of Pure and Applied Logic 86 (1):47-100.

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