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A Note on the Set-Theoretic Representation of Arbitrary Lattices

K. Dosen
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Abstract

Every lattice is isomorphic to a lattice whose elements are sets of sets, and whose operations are intersection and an operation extending the union of two sets of sets A and B by the set of all sets in which the intersection of an element of A and of an element of B is included. This representation spells out precisely Birkhoff's and Frinks's representation of arbitrary lattices, which is related to Stone's set-theoretic representation of distributive lattices.

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K. Dosen. 2003-03-01. A Note on the Set-Theoretic Representation of Arbitrary Lattices. https://arxiv.org/abs/math/0303005

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