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- Birkhoffs_representation_theorem abstract "This is about lattice theory. For other similarly named results, see Birkhoff's theorem (disambiguation).In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations correspond to unions and intersections of sets. The theorem can be interpreted as providing a one-to-one correspondence between distributive lattices and partial orders, between quasi-ordinal knowledge spaces and preorders, or between finite topological spaces and preorders. It is named after Garrett Birkhoff, who published a proof of it in 1937.The name “Birkhoff's representation theorem” has also been applied to two other results of Birkhoff, one from 1935 on the representation of Boolean algebras as families of sets closed under union, intersection, and complement (so-called fields of sets, closely related to the rings of sets used by Birkhoff to represent distributive lattices), and Birkhoff's HSP theorem representing algebras as products of irreducible algebras. Birkhoff's representation theorem has also been called the fundamental theorem for finite distributive lattices.".
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- Birkhoffs_representation_theorem wikiPageWikiLink 2-satisfiability.
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- Birkhoffs_representation_theorem wikiPageWikiLink Independent_set_(graph_theory).
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- Birkhoffs_representation_theorem wikiPageWikiLink Union_(set_theory).
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- Birkhoffs_representation_theorem wikiPageWikiLink Variety_(universal_algebra).
- Birkhoffs_representation_theorem wikiPageWikiLink File:Birkhoff120.svg.
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- Birkhoffs_representation_theorem wikiPageWikiLinkText "Birkhoff's representation theorem".
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- Birkhoffs_representation_theorem subject Category:Lattice_theory.
- Birkhoffs_representation_theorem subject Category:Theorems_in_algebra.
- Birkhoffs_representation_theorem comment "This is about lattice theory. For other similarly named results, see Birkhoff's theorem (disambiguation).In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations correspond to unions and intersections of sets.".
- Birkhoffs_representation_theorem label "Birkhoff's representation theorem".
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