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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 25)
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About this book
There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the develop ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2J and HERMES [1]. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No know ledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs.
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Table of contents (2 chapters)
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Front Matter
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Back Matter
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Bibliographic Information
Book Title: Boolean Algebras
Authors: Roman Sikorski
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
DOI: https://doi.org/10.1007/978-3-642-85820-8
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1969
Softcover ISBN: 978-3-642-85822-2Published: 09 April 2012
eBook ISBN: 978-3-642-85820-8Published: 06 December 2012
Edition Number: 3
Number of Pages: X, 240
Topics: Mathematical Logic and Foundations, Mathematical Logic and Formal Languages