Computing coproducts of finitely presented Gödel algebras

Abstract We obtain an algorithm to compute finite coproducts of finitely generated Godel algebras, i.e. Heyting algebras satisfying the prelinearity axiom ( α → β ) ∨ ( β → α ) = 1 . (Since Godel algebras are locally finite, ‘finitely generated’, ‘finitely presented’, and ‘finite’ have identical meaning in this paper.) We achieve this result using ordered partitions of finite sets as a key tool to investigate the category opposite to finitely generated Godel algebras (forests and open order-preserving maps). We give two applications of our main result. We prove that finitely presented Godel algebras have free products with amalgamation; and we easily obtain a recursive formula for the cardinality of the free Godel algebra over a finite number of generators first established by A. Horn.