A Note on the Set-Theoretic Representation of Arbitrary Lattices
Logic
2007-05-23 v1
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.
Cite
@article{arxiv.math/0303005,
title = {A Note on the Set-Theoretic Representation of Arbitrary Lattices},
author = {K. Dosen},
journal= {arXiv preprint arXiv:math/0303005},
year = {2007}
}
Comments
3 pages (published in A. Krapez ed., A Tribute to S.B. Presic, Mathematical Institute, Belgrade, 2001, pp. 99-101)