Model-completion of varieties of co-Heyting algebras

by L. Darnière and M. Junker

Houston Journal of Mathematics 44 (2018) no. 1, 49-82

Abstract

It is known that exactly eight varieties of Heyting algebras have a model-completion. However no concrete axiomatization of these model-completions were known by now except for the trivial variety (reduced to the one-point algebra) and the variety of Boolean algebras. For each of the six remaining varieties we introduce two axioms and show that 1) these axioms are satisfied by all the algebras in the model-completion, and 2) all the algebras in this variety satisfying these two axioms satisfy a certain remarkable embedding theorem. For four of these six varieties (those which are locally finite) these two results provide a new proof of the existence of a model-completion with, in addition, an explicit and finite axiomatization.

Mathematics Subject Classification

06D20 Heyting algebras [See also 03G25]
03C60 Model-theoretic algebra [See also 08C10, 11U09, 12L12, 13L05, 16B70, 20A15]

Electronic version of the paper

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