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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle (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.