Boolean Algebras

  • Authors
  • Roman Sikorski

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 25)

Table of contents

  1. Front Matter
    Pages II-X
  2. Roman Sikorski
    Pages 1-2
  3. Roman Sikorski
    Pages 3-54
  4. Roman Sikorski
    Pages 54-190
  5. Back Matter
    Pages 191-237

About these proceedings

Introduction

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 [IJ. 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.

Keywords

Boolean algebra Boolescher Verband Finite Mathematica Morphism algebra function logic mathematical logic proof set theory theorem topology

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-01507-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1960
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-01509-4
  • Online ISBN 978-3-662-01507-0
  • About this book