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

Abstract :

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.

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https://hal.univ-angers.fr/hal-03031611
Contributeur : Okina Université d'Angers <>
Soumis le : lundi 30 novembre 2020 - 15:21:02
Dernière modification le : mardi 1 juin 2021 - 21:06:04

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Luck Darnière, Markus Junker. On Bellissima’s construction of the finitely generated free Heyting algebras, and beyond. Archive for Mathematical Logic, Springer Verlag, 2010, 49 (7-8), pp.743 - 771. ⟨10.1007/s00153-010-0194-7⟩. ⟨hal-03031611⟩

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