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,Model theory of probability spaces, Model theory of operator algebras, De Gruyter Ser
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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.