Distributive lattices in o-minimal structures
Authors: Zoltan A. Kocsis
Abstract: We investigate distributive lattices and Heyting algebras definable in o-minimal structures. We give a complete description of one-dimensional bounded distributive lattices definable over an o-minimal structure expanding a real-closed field, and prove a definable analogue of Birkhoff representation, which we use to classify all one-variable equations in the language of Heyting algebras with respect to whether they can be satisfied in a maximal-dimension subset of a given algebra.
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