Introduction to Boolean Algebras

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Sprache: Englisch

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Beschreibung

This book is an informal yet systematic presentation of lectures given by the author on Boolean algebras. The author's style is characteristically bold and fresh. He treats Boolean algebras, develops some intriguing ideas, and provides rare insights. Exercises are generously sprinkled through the text for course study. The second edition has been greatly expanded and rewritten, specific changes include:

* More detail explanations of the material in every section, making the text more accessible to undergraduates

* Three times as many exercises as well as a solutions manual

* A more careful explanation of the relationship between Boolean rings and Boolean algebras has been added;

* thirteen new chapters, including ones on topology and continuous functions and others on the extension theorem for homomorphisms, congruences and quotient algebras, lattice of ideals, and duality theory for products.

Über den Autor

Steven Givant is a Professor of Mathematics and Computer Science at Mills College, California. As a long-term collaborator of Alfred Tarski-one of the great logicians-Givant has been involved first-hand in the development of the field of relation algebras since the 1970s. His previous books include Duality Theories for Boolean Algebras with Operators (Springer, 2014), Introduction to Boolean Algebras, with Paul Halmos (Springer, 2009), Logic as Algebra, with Paul Halmos (MAA, 1998), and A Formalization of Set Theory without Variables, with Alfred Tarski (AMS, 1987). He was also coeditor, with Ralph McKenzie, of Alfred Tarski's Collected Papers: Vol 1-4 (Birkhäuser, 1986).

Zusammenfassung

* More detail explanations of the material in every section, making the text more accessible to undergraduates

* Three times as many exercises as well as a solutions manual

* A more careful explanation of the relationship between Boolean rings and Boolean algebras has been added;

* thirteen new chapters, including ones on topology and continuous functions and others on the extension theorem for homomorphisms, congruences and quotient algebras, lattice of ideals, and duality theory for products.

Inhaltsverzeichnis

Boolean Rings.- Boolean Algebras.- Boolean Algebras Versus Rings.- The Principle of Duality.- Fields of Sets.- Elementary Relations.- Order.- Infinite Operations.- Topology.- Regular Open Sets.- Subalgebras.- Homomorphisms.- Extensions of Homomorphisms.- Atoms.- Finite Boolean Algebras.- Atomless Boolean Algebras.- Congruences and Quotients.- Ideals and Filters.- Lattices of Ideals.- Maximal Ideals.- Homomorphism and Isomorphism Theorems.- The Representation Theorem.- Canonical Extensions.- Complete Homomorphisms and Complete Ideals.- Completions.- Products of Algebras.- Isomorphisms of Factors.- Free Algebras.- Boolean s-algebras.- The Countable Chain Condition.- Measure Algebras.- Boolean Spaces.- Continuous Functions.- Boolean Algebras and Boolean Spaces.- Duality for Ideals.- Duality for Homomorphisms.- Duality for Subalgebras.- Duality for Completeness.- Boolean s-spaces.- The Representation of s-algebras.- Boolean Measure Spaces.- Incomplete Algebras.- Duality for Products.- Sums of Algebras.- Isomorphisms of Countable Factors.

Details

Erscheinungsjahr:	2010
Fachbereich:	Grundlagen
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiv 574 S. 10 s/w Illustr. 574 p. 10 illus.
ISBN-13:	9781441923240
ISBN-10:	1441923241
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Givant, Steven Halmos, Paul
Hersteller:	Springer Copernicus Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 32 mm
Von/Mit:	Steven Givant (u. a.)
Erscheinungsdatum:	19.11.2010
Gewicht:	0,879 kg