Category: Theorems in lattice theory

Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: , where is any Boolean function, is a variable, is the complement of , and and are with the arg

In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement for filters on sets is known as the ultrafilter l

In Boolean algebra, the consensus theorem or rule of consensus is the identity: The consensus or resolvent of the terms and is . It is the conjunction of all the unique literals of the terms, excludin

In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental to the deeper understanding o

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 lattic

In mathematical economics, Topkis's theorem is a result that is useful for establishing comparative statics. The theorem allows researchers to understand how the optimal value for a choice variable ch