In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties...

a list of topics around Boolean algebra and propositional logic. Algebra of sets Boolean algebra (structure) Boolean algebra Field of sets Logical connective...

In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the...

Look up Boolean algebra in Wiktionary, the free dictionary. Boolean algebra is the algebra of truth values and operations on them. Boolean algebra may also...

free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that: Each element of the Boolean algebra can be...

interior algebra is an algebraic structure with the signature ⟨S, ·, +, ′, 0, 1, I⟩ where ⟨S, ·, +, ′, 0, 1⟩ is a Boolean algebra and postfix I designates...

(usually "true" and "false") Boolean algebra, a logical calculus of truth values or set membership Boolean algebra (structure), a set with operations resembling...

In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with...

In abstract algebra, a monadic Boolean algebra is an algebraic structure A with signature ⟨·, +, ', 0, 1, ∃⟩ of type ⟨2,2,1,0,0,1⟩, where ⟨A, ·, +, ',...

In mathematics, an algebraic structure or algebraic system consists of a nonempty set A (called the underlying set, carrier set or domain), a collection...

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...

Topological Boolean algebra may refer to: In abstract algebra and mathematical logic, topological Boolean algebra is one of the many names that have been...

abstract algebra, a derivative algebra is an algebraic structure of the signature <A, ·, +, ', 0, 1, D> where <A, ·, +, ', 0, 1> is a Boolean algebra and D...

An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction...

residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the monoid...

play an essential role in the representation theory of Boolean algebras. Every Boolean algebra can be represented as a field of sets. A field of sets...

algebra Kleene algebra (with involution) Łukasiewicz–Moisil algebra Boolean algebra (structure) Boolean ring Complete Boolean algebra Orthocomplemented...

Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued...

Boolean arithmetic; The primary algebra (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean...

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

Morgan laws, either law implies the other, and an algebra which satisfies them becomes a Boolean algebra. Remark: It follows that ¬(x ∨ y) = ¬x ∧ ¬y, ¬1...

and the algebraic structure which are its models are shown on the right in the same row. Some of these structures are either Boolean algebras or proper...

countable choice Axiom of dependent choice Zorn's lemma Boolean algebra (structure) Boolean-valued model Burali-Forti paradox Cantor's back-and-forth...

algebra, in which a set of finitary relations that is closed under certain operators Boolean algebra and Boolean algebra (structure) Heyting algebra In...

This is comparable to the role Boolean algebras play for propositional logic. Cylindric algebras are Boolean algebras equipped with additional cylindrification...

\scriptstyle \land } a = a). Examples of lattices include Heyting algebras and Boolean algebras, in particular sets of sets with union (∪) and intersection...

remainder theorem Field (mathematics) Algebraic number field Polynomial ring Integral domain Boolean algebra (structure) Principal ideal domain Euclidean...

"true" and "false", but instead take values in some fixed complete Boolean algebra. Boolean-valued models were introduced by Dana Scott, Robert M. Solovay...

tables. Philosophy portal Binary logic (disambiguation) Boolean algebra (structure) Boolean function Digital circuit Four-valued logic Homogeneity (linguistics)...

algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures...