On the model-completion of Heyting algebras
Logic
2018-10-04 v1
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.
Keywords
Cite
@article{arxiv.1810.01704,
title = {On the model-completion of Heyting algebras},
author = {Luck Darnière},
journal= {arXiv preprint arXiv:1810.01704},
year = {2018}
}