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.
An Introduction To Continuous Model Theory
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We present an introduction to modern continuous model theory with an emphasis on its interactions with topics covered in this volume such as $C^*$-algebras and von Neumann algebras. The role of ultraproducts is highlighted and expositions of definable sets, imaginaries, quantifier elimination and separable categoricity are included.
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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.