On the model-completion of Heyting algebras

Luck Darnière (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

We axiomatize the model-completion of the theory of Heyting algebras by means of the "Density" and "Splitting" properties in [DJ18], and of a certain "QE Property" that we introduce here. In addition: we prove that this model-completion has a prime model, which is locally finite and which we explicitly construct; we show how the Open Mapping Theorem of [vGR18] can be derived from the QE Property of existentially closed Heyting algebras; and we construct a certain "discriminant" for equations in Heyting algebras, similar to its ring theoretic counterpart.

Mots clés: Heyting algebra; quantifier elimination; decidability; model-completion; uniform interpolant; open mapping; discriminant

Domaines: Logique [math.LO]

Luck Darnière. On the model-completion of Heyting algebras. 2018. ⟨hal-01885531⟩