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arXiv · 1810.01704

On the model-completion of Heyting algebras

Luck Darnière
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Abstract

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.

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Luck Darnière. 2018-10-03. On the model-completion of Heyting algebras. https://arxiv.org/abs/1810.01704

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