Archive for Mathematical Logic 49 (7-8):743-771 (2010)

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
Keywords Free Heyting algebras  Finitely generated Heyting algebras  Completion  Irreducible elements  Spectrum  Kripke model  Automorphism group
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DOI 10.1007/s00153-010-0194-7
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Model Theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
Intuitionistic Logic, Model Theory and Forcing.Melvin Fitting - 1969 - Amsterdam: North-Holland Pub. Co..
Finitely Generated Free Heyting Algebras.Fabio Bellissima - 1986 - Journal of Symbolic Logic 51 (1):152-165.

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The Admissible Rules of ${{Mathsf{BD}_{2}}}$ and ${Mathsf{GSc}}$.Jeroen P. Goudsmit - 2018 - Notre Dame Journal of Formal Logic 59 (3):325-353.

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Finitely Generated Free Heyting Algebras.Fabio Bellissima - 1986 - Journal of Symbolic Logic 51 (1):152-165.
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