On Bellissima’s construction of the finitely generated free Heyting algebras, and beyond

TitreOn Bellissima’s construction of the finitely generated free Heyting algebras, and beyond
Type de publicationArticle de revue
AuteurDarniere, Jack-Luck , Junker, Markus
PaysAllemagne
EditeurSpringer
VilleBerlin
TypeArticle scientifique dans une revue à comité de lecture
Année2010
LangueAnglais
DateDec 2010
Numéro7-8
Pagination743 - 771
Volume49
Titre de la revueArchive for Mathematical Logic
ISSN1432-0665
Mots-clésAlgebra, Automorphism group, Completion, Finitely generated Heyting algebras, Free Heyting algebras, Irreducible elements, Kripke model, Mathematical Logic and Foundations, Mathematics, general, Spectrum
Résumé en anglais

We study finitely generated free Heyting algebras from a topological and from a model theoretic point of view. We review Bellissima’s representation of the finitely generated free Heyting algebra; we prove that it yields an embedding in the profinite completion, which is also the completion with respect to a naturally defined metric. We give an algebraic interpretation of the Kripke model used by Bellissima as the principal ideal spectrum and show it to be first order interpretable in the Heyting algebra, from which several model theoretic and algebraic properties are derived. In particular, we prove that a free finitely generated Heyting algebra has only one set of free generators, which is definable in it. As a consequence its automorphism group is the permutation group over its generators.

URL de la noticehttp://okina.univ-angers.fr/publications/ua108
DOI10.1007/s00153-010-0194-7
Lien vers le document

http://hal.archives-ouvertes.fr/hal-00346039