Boolean Algebras

1. Front Matter

   Pages II-X

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2. Terminology and notation

   • Roman Sikorski

   Pages 1-2

3. Finite joins and meets

   • Roman Sikorski

   Pages 3-54

4. Infinite joins and meets

   • Roman Sikorski

   Pages 54-190

5. Back Matter

   Pages 191-237

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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.

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