# Category: Theorems in lattice theory

Boole's expansion theorem
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
Boolean prime ideal theorem
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
Consensus theorem
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
Stone's representation theorem for Boolean algebras
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
Birkhoff's representation theorem
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
Topkis's theorem
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