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...

of two. Stone's celebrated representation theorem for Boolean algebras states that every Boolean algebra A is isomorphic to the Boolean algebra of all...

law Stone's representation theorem for Boolean algebras Boole, George De Morgan, Augustus Jevons, William Stanley Peirce, Charles Sanders Stone, Marshall...

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...

that included Stone's representation theorem for Boolean algebras, an important result in mathematical logic, topology, universal algebra and category...

collected under the label Stone duality, since they form a natural generalization of Stone's representation theorem for Boolean algebras. These concepts are...

Stone's theorem may refer to a number of theorems of Marshall Stone: Stone's representation theorem for Boolean algebras Stone–Weierstrass theorem Stone–von...

_{0}} . For more on this topological approach to free Boolean algebra, see Stone's representation theorem for Boolean algebras. Boolean algebra (structure)...

spaces. Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a field of sets. A variant, Stone's representation...

Shannon's expansion theorem (Boolean algebra) Stone's representation theorem for Boolean algebras (mathematical logic) Szpilrajn extension theorem (axiom of choice)...

{\displaystyle b\in B.} Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to the Boolean algebra of clopen sets...

defined via Boolean algebras in a way that the tautologies (theorems) of propositional logic correspond to equational theorems of Boolean algebra. Syntactically...

countable unions Stone duality – Relationship between certain categories Stone's representation theorem for Boolean algebras – Every Boolean algebra is isomorphic...

important tool in many applications of order theory. In Stone's representation theorem for Boolean algebras, the maximal ideals (or, equivalently via the negation...

by algebras of the type appearing in the Stone–Weierstrass theorem and described below. A different generalization of Weierstrass' original theorem is...

This theorem is also equivalent (via Stone's representation theorem for Boolean algebras) to the fact that any two countable atomless Boolean algebras are...

axiom of choice). Stone's representation theorem for Boolean algebras needs the Boolean prime ideal theorem. The Nielsen–Schreier theorem, that every subgroup...

some parameters A {\displaystyle A} is a Boolean algebra. By Stone's representation theorem for Boolean algebras there is a natural dual topological space...

what Boolean algebras are to set theory and ordinary propositional logic. Interior algebras form a variety of modal algebras. An interior algebra is an...

with these operations any field of sets is a Boolean ring. By Stone's representation theorem every Boolean ring is isomorphic to a field of sets (treated...

the weakest proposition for which modus ponens, the inference rule A → B, A ⊢ B, is sound. Like Boolean algebras, Heyting algebras form a variety axiomatizable...

lattices. Representation theorem Birkhoff's representation theorem Stone's representation theorem for Boolean algebras Stone duality Esakia duality Stone (1938)...

Suslin's problem Absorption law Prewellordering Stone duality Stone's representation theorem for Boolean algebras Specialization (pre)order Order topology of...

well-known theorem of this kind is Stone's representation theorem for Boolean algebras, which is a special instance within the general scheme of Stone duality...

algebra is representable is a fundamental way RA differs from QRA and Boolean algebras, which, by Stone's representation theorem for Boolean algebras...

of algebras of sets under union and complementation.' Just as group theory deals with groups, and linear algebra with vector spaces, Boolean algebras are...

Intrinsic metric Category of metric spaces Stone duality Stone's representation theorem for Boolean algebras Specialization (pre)order Sober space Spectral space...

“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...

for these deductive systems) and connected problems like representation and duality. Well known results like the representation theorem for Boolean algebras...

isomorphism. These were originally proved by considering Boolean algebras and applying Stone duality. Jan van Mill has described βN as a "three headed...