Godel algebras free over finite distributive lattices

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Authors:
Stefano Aguzzoli
Brunella Gerla
Vincenzo Marra
Title: Godel algebras free over finite distributive lattices
Journal: Annals of Pure and Applied Logic
Volume 155
Number
Pages: 183-193
Year: 2008




Abstract

Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom (x \to y) \vee (y \to x)=\top. 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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