Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom Formula Not Shown . 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.
Gödel Algebras Free over Finite Distributive Lattices / S. Aguzzoli, B. Gerla, V. Marra. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - 155:3(2008 Oct), pp. 183-193. [10.1016/j.apal.2008.04.003]
Gödel Algebras Free over Finite Distributive Lattices
S. AguzzoliPrimo
;V. MarraUltimo
2008
Abstract
Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom Formula Not Shown . 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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