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arXiv · 2606.19506

Distributive lattices in o-minimal structures

Zoltan A. Kocsis
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Abstract

We investigate distributive lattices and Heyting algebras definable in o-minimal structures. We give a complete description of one-dimensional distributive lattices definable in o-minimal structures expanding a real-closed field, and prove a definable analogue of Birkhoff representation. As applications, we obtain a sharp lower bound on the dimension of definable Heyting algebras which contain infinite free subalgebras, and determine all one-variable equations in the language of Heyting algebras whose solution set can constitute a maximal-dimension proper subset of an infinite algebra.

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Zoltan A. Kocsis. 2026-06-17. Distributive lattices in o-minimal structures. https://arxiv.org/abs/2606.19506

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