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Books > Science & Mathematics > Mathematics > Algebra
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Introduction to Boolean Algebras (Paperback, Softcover reprint of hardcover 1st ed. 2009)
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Introduction to Boolean Algebras (Paperback, Softcover reprint of hardcover 1st ed. 2009)
Series: Undergraduate Texts in Mathematics
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The theory of Boolean algebras was created in 1847 by the English
mat- matician George Boole. He conceived it as a calculus (or
arithmetic) suitable for a mathematical analysis of logic. The form
of his calculus was rather di?erent from the modern version, which
came into being during the - riod 1864-1895 through the
contributions of William Stanley Jevons, Aug- tus De Morgan,
Charles Sanders Peirce, and Ernst Schr. oder. A foundation of the
calculus as an abstract algebraic discipline, axiomatized by a set
of equations, and admitting many di?erent interpretations, was
carried out by Edward Huntington in 1904. Only with the work of
Marshall Stone and Alfred Tarski in the 1930s, however, did Boolean
algebra free itself completely from the bonds of logic and become a
modern mathematical discipline, with deep theorems and -
portantconnections toseveral otherbranchesofmathematics,
includingal- bra,analysis, logic, measuretheory, probability
andstatistics, settheory, and topology. For instance, in logic,
beyond its close connection to propositional logic, Boolean algebra
has found applications in such diverse areas as the proof of the
completeness theorem for ?rst-order logic, the proof of the Lo ' s
conjecture for countable ? rst-order theories categorical in power,
and proofs of the independence of the axiom of choice and the
continuum hypothesis ? in set theory. In analysis, Stone's
discoveries of the Stone-Cech compac- ?cation and the
Stone-Weierstrass approximation theorem were intimately connected
to his study of Boolean algebras.
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