Submission date: 18 December 2008.

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 show that the Kripke model used by Bellissima is first order interpretable in the Heyting algebra, from which several model theoretic and algebraic properties are derived.

Mathematics Subject Classification: 06D20, 03C64, 06B23, 06B30, 08B20

Keywords and phrases: free Heyting algebras, finitely generated Heyting algebras, completion, irreducible elements, spectrum, Kripke model, automorphism group

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