Gödel algebras free over finite distributive lattices

Annals of Pure and Applied Logic 155 (3):183-193 (2008)
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Abstract

Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom =. In 1969, Horn proved that a Heyting algebra is a Gödel algebra if and only if its set of prime filters partially ordered by reverse inclusion–i.e. its prime spectrum–is a forest. Our main result characterizes Gödel algebras that are free over some finite distributive lattice by an intrisic property of their spectral forest

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Free l-algebras.Alfred Horn - 1969 - Journal of Symbolic Logic 34 (3):475-480.

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