# A Note on the Set-Theoretic Representation of Arbitrary Lattices

Source: [A Note on the Set-Theoretic Representation of Arbitrary Lattices](<https://www.sota2.com/research/paper/68fa4cc51e209131ce94f1ef>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T08:57:20.132Z

Authors: K. Dosen

Published: 2003-03-01T12:19:46.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0303005>)

[PDF](<https://arxiv.org/pdf/math/0303005.pdf>)