Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Kocsis, Zoltan A.
Institution: UNSW Sydney
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165379803
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