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On the model-completion of Heyting algebras

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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Contributor : Luck Darnière Connect in order to contact the contributor
Submitted on : Tuesday, October 2, 2018 - 9:01:01 AM
Last modification on : Wednesday, November 3, 2021 - 9:18:33 AM
Long-term archiving on: : Thursday, January 3, 2019 - 1:15:02 PM


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  • HAL Id : hal-01885531, version 1
  • ARXIV : 1810.01704



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



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