We obtain an algorithm to compute finite coproducts of finitely generated Gödel algebras, i.e. Heyting algebras satisfying the prelinearity axiom (α→β)logical or(β→α)=1. (Since Gödel 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 Gödel algebras (forests and open order-preserving maps). 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.

Computing coproducts of finitely presented Gödel algebras / O. D'Antona, V. Marra. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - 142:1-3(2006), pp. 202-211.

Computing coproducts of finitely presented Gödel algebras

O. D'Antona
Primo
;
V. Marra
Ultimo
2006

Abstract

We obtain an algorithm to compute finite coproducts of finitely generated Gödel algebras, i.e. Heyting algebras satisfying the prelinearity axiom (α→β)logical or(β→α)=1. (Since Gödel 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 Gödel algebras (forests and open order-preserving maps). 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.
Coproducts; Forests; Gödel algebras; Heyting algebras; Open maps; Ordered partitions; Trees
Settore INF/01 - Informatica
Settore MAT/01 - Logica Matematica
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/19765
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 28
  • ???jsp.display-item.citation.isi??? 25
social impact