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This is a list of topics around Boolean algebra and propositional logic. Articles with a wide scope and introductions. Algebra of sets; Boolean algebra (structure)
This is a list of mathematical logic topics. For traditional syllogistic logic, see the list of topics in logic . See also the list of computability and complexity topics for more theory of algorithms .
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 variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
Discrete algebras include: Boolean algebra used in logic gates and programming; relational algebra used in databases; discrete and finite versions of groups, rings and fields are important in algebraic coding theory; discrete semigroups and monoids appear in the theory of formal languages.
Algebra of sets; Axiom of choice. Axiom of countable choice; Axiom of dependent choice; Zorn's lemma; Axiom of power set; Boolean-valued model; Burali-Forti paradox; Cantor's back-and-forth method; Cantor's diagonal argument; Cantor's first uncountability proof; Cantor's paradox; Cantor's theorem; Cantor–Bernstein–Schroeder theorem ...
The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854.
Algebra includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called group .
For a complete boolean algebra infinite de-Morgan's laws hold. A Boolean algebra is complete if and only if its Stone space of prime ideals is extremally disconnected. Sikorski's extension theorem states that if A is a subalgebra of a Boolean algebra B, then any homomorphism from A to a complete Boolean algebra C can be extended to a morphism ...