Handbook of Boolean algebras

Author(s)

• Monk, James Donald
• Bonnet, Robert
• Koppelberg, Sabine

Bibliographic Information

Handbook of Boolean algebras

edited by J. Donald Monk, with the cooperation of Robert Bonnet

North-Holland , Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1989

• : set
• v. 1
• v. 2
• v. 3

Note

Includes bibliographies and indexes

Vol. 1 by Sabine Koppelberg

Description and Table of Contents

Volume

v. 1 ISBN 9780444702616

Description

This Handbook treats those parts of the theory of Boolean algebras of most interest to pure mathematicians: the set-theoretical abstract theory and applications and relationships to measure theory, topology, and logic. It is divided into two parts (published in three volumes). Part I (volume 1) is a comprehensive, self-contained introduction to the set-theoretical aspects of the theory of Boolean Algebras. It includes, in addition to a systematic introduction of basic algebra and topological ideas, recent developments such as the Balcar-Franek and Shelah-Shapirovskii results on free subalgebras. Part II (volumes 2 and 3) contains articles on special topics describing - mostly with full proofs - the most recent results in special areas such as automorphism groups, Ketonen's theorem, recursive Boolean algebras, and measure algebras.

Table of Contents

I. General Theory of Boolean Algebras (S. Koppelberg). Elementary Arithmetic. Algebraic Theory. Topological Duality. Free Constructions. Infinite Operations. Special Classes of Boolean Algebras. Metamathematics. References. Index.

Volume

v. 2 ISBN 9780444871527

Description

This Handbook treats those parts of the theory of Boolean algebras of most interest to pure mathematicians: the set-theoretical abstract theory and applications and relationships to measure theory, topology, and logic. It is divided into two parts (published in three volumes). Part I (volume 1) is a comprehensive, self-contained introduction to the set-theoretical aspects of the theory of Boolean Algebras. It includes, in addition to a systematic introduction of basic algebra and topological ideas, recent developments such as the Balcar-Franek and Shelah-Shapirovskii results on free subalgebras. Part II (volumes 2 and 3) contains articles on special topics describing - mostly with full proofs - the most recent results in special areas such as automorphism groups, Ketonen's theorem, recursive Boolean algebras, and measure algebras.

Table of Contents

II. Topics in the Theory of Boolean Algebras. Arithmetical Properties of Boolean Algebras: Distributive Laws (T. Jech). Disjoint Refinement (B. Balcar, P. Simon). Algebraic Properties of Boolean Algebras: Subalgebras (R. Bonnet). Cardinal Functions on Boolean Spaces (E.K. van Douwen). The Number of Boolean Algebras (J.D. Monk). Endomorphisms of Boolean Algebras (J.D. Monk). Automorphism Groups (J.D. Monk). On the Reconstruction of Boolean Algebras from their Automorphism Groups (M. Rubin). Embeddings and Automorphisms (P. St panek). Rigid Boolean Algebras (M. Bekkali, R. Bonnet). Homogeneous Boolean Algebras (P. St panek, M. Rubin). References. Index.

Volume

v. 3 ISBN 9780444871534

Description

This Handbook treats those parts of the theory of Boolean algebras of most interest to pure mathematicians: the set-theoretical abstract theory and applications and relationships to measure theory, topology, and logic. It is divided into two parts (published in three volumes). Part I (volume 1) is a comprehensive, self-contained introduction to the set-theoretical aspects of the theory of Boolean Algebras. It includes, in addition to a systematic introduction of basic algebra and topological ideas, recent developments such as the Balcar-Franek and Shelah-Shapirovskii results on free subalgebras. Part II (volumes 2 and 3) contains articles on special topics describing - mostly with full proofs - the most recent results in special areas such as automorphism groups, Ketonen's theorem, recursive Boolean algebras, and measure algebras.

Table of Contents

Special Classes of Boolean Algebras: Superatomic Boolean Algebras (J. Roitman). Projective Boolean Algebras (S. Koppelberg). Countable Boolean Algebras (R.S. Pierce). Measure Algebras (D.H. Fremlin). Logical Questions: Decidable Extensions of the Theory of Boolean Algebras (M. Weese). Undecidable Extensions of the Theory of Boolean Algebras (M. Weese). Recursive Boolean Algebras (J.B. Remmel). Lindenbaum-Tarski Algebras (D. Myers). Boolean-Valued Models (T. Jech). Appendix on Set Theory (J.D. Monk). Chart of Topological Duality. Appendix on General Topology (B. Balcar, P. Simon). References. Bibliography. Index.

by "Nielsen BookData"

Details

• NCID: BA0670060X
• ISBN:
  • 0444872914
  • 044470261X
  • 0444871527
  • 0444871535
• LCCN: 88025140
• Country Code: ne
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Amsterdam ; Tokyo,New York, N.Y., U.S.A.
• Pages/Volumes: 3 v.
• Size: 25 cm
• Classification:
  • LCC : QA10.3
  • DC19 : 511.3/24
• Subject Headings:
  • LCSH : Algebra, Boolean -- Handbooks, manuals, etc