Infinite pseudofinite limits of partition lattices have a definable Boolean sublattice of modular elements, and each element is determined by its set of modular selectors.
Ward Henson, and Alexander Usvyatsov,Model theory for metric structures, Model theory with applications to algebra and analysis
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The model theory of metric lattices: pseudofinite partition lattices
Infinite pseudofinite limits of partition lattices have a definable Boolean sublattice of modular elements, and each element is determined by its set of modular selectors.