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

by L. Darnière and M. Junker

Archive for Mathematical Logic 49 (2010), no. 7-8, 743–771

Submitted on December 8, 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 Heyting algebras [See also 03G25]
03C60 Model-theoretic algebra [See also 08C10, 11U09, 12L12, 13L05, 16B70, 20A15]
06B23 Complete lattices, completions
06B30 Topological lattices, order topologies [See also 06F30, 22A26, 54F05, 54H12]
08B20 Free algebras

Electronic version of the paper

Version December 2008 (24 pages) pdf