Computing coproducts of finitely presented Gödel algebras

Annals of Pure and Applied Logic 142 (1):202-211 (2006)


We obtain an algorithm to compute finite coproducts of finitely generated Gödel algebras, i.e. Heyting algebras satisfying the prelinearity axiom =1. We achieve this result using ordered partitions of finite sets as a key tool to investigate the category opposite to finitely generated Gödel algebras . We give two applications of our main result. We prove that finitely presented Gödel algebras have free products with amalgamation; and we easily obtain a recursive formula for the cardinality of the free Gödel algebra over a finite number of generators first established by A. Horn

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References found in this work

Logic with Truth Values in a Linearly Ordered Heyting Algebra.Alfred Horn - 1969 - Journal of Symbolic Logic 34 (3):395-408.
Free L-Algebras.Alfred Horn - 1969 - Journal of Symbolic Logic 34 (3):475-480.

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