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Book synopsis

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.

Book details

Book category Books in English Computing & information technology Computer science Mathematical theory of computation

• Full title: Boolean Algebras, 1
• Author: Roman Sikorski
• Language: English
• Binding: Paperback
• Number of pages: 240
• EAN: 9783642858222
• ISBN: 3642858228
• ID: 02004899
• Publisher: Springer, Berlin
• Weight: 391 g
• Dimensions: 235 × 155 × 19 mm
• Date of publishing: 09. April 2012

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