Author: Publisher:
ISBN:
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Languages : en
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Book Description
Handbook of Boolean Algebras
Author: Handbook of Boolean Algebras
Author: Robert BonnetPublisher:
ISBN: 9780444872913
Category : Algebra, Boolean
Languages : en
Pages : 650
Book Description
Introduction to Boolean Algebras
Author: Steven GivantPublisher: Springer Science & Business Media
ISBN: 0387402934
Category : Mathematics
Languages : en
Pages : 589
Book Description
This book is an informal though systematic series of lectures on Boolean algebras. It contains background chapters on topology and continuous functions and includes hundreds of exercises as well as a solutions manual.
Handbook of Boolean Algebras
Author: Sabine KoppelbergPublisher:
ISBN: 9780444872913
Category : Algebra, Boolean
Languages : en
Pages : 312
Book Description
Cardinal Invariants on Boolean Algebras
Author: J. Donald MonkPublisher: Springer Science & Business Media
ISBN: 3034807309
Category : Mathematics
Languages : en
Pages : 573
Book Description
This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of the earlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping number. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including interval algebras, tree algebras and superatomic algebras.
Boolean Algebras
Author: Roman SikorskiPublisher: Springer Science & Business Media
ISBN: 3642858201
Category : Mathematics
Languages : en
Pages : 248
Book Description
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.
Lectures on Boolean Algebras
Author: Paul R. HalmosPublisher: Courier Dover Publications
ISBN: 0486834573
Category : Mathematics
Languages : en
Pages : 160
Book Description
Concise and informal as well as systematic, this presentation on the basics of Boolean algebra has ranked among the fundamental books on the subject since its initial publication in 1963.
Boolean Algebras in Analysis
Author: D.A. VladimirovPublisher: Springer Science & Business Media
ISBN: 940170936X
Category : Mathematics
Languages : en
Pages : 614
Book Description
Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting classical theorems, the book describes the topologies and uniform structures of Boolean algebras, the basics of complete Boolean algebras and their continuous homomorphisms, as well as lifting theory. The first part also includes an introductory chapter describing the elementary to the theory. The second part deals at a graduate level with the metric theory of Boolean algebras at a graduate level. The covered topics include measure algebras, their sub algebras, and groups of automorphisms. Ample room is allotted to the new classification theorems abstracting the celebrated counterparts by D.Maharam, A.H. Kolmogorov, and V.A.Rokhlin. Boolean Algebras in Analysis is an exceptional definitive source on Boolean algebra as applied to functional analysis and probability. It is intended for all who are interested in new and powerful tools for hard and soft mathematical analysis.
Cardinal Invariants on Boolean Algebras
Author: J. Donald MonkPublisher: Springer Science & Business Media
ISBN: 3034603347
Category : Mathematics
Languages : en
Pages : 308
Book Description
This text covers cardinal number valued functions defined for any Boolean algebra such as cellularity. It explores the behavior of these functions under algebraic operations such as products, free products, ultraproducts and their relationships to each other.
Countable Boolean Algebras and Decidability
Author: Sergey GoncharovPublisher: Springer Science & Business Media
ISBN: 9780306110610
Category : Mathematics
Languages : en
Pages : 344
Book Description
This book describes the latest Russian research covering the structure and algorithmic properties of Boolean algebras from the algebraic and model-theoretic points of view. A significantly revised version of the author's Countable Boolean Algebras (Nauka, Novosibirsk, 1989), the text presents new results as well as a selection of open questions on Boolean algebras. Other current features include discussions of the Kottonen algebras in enrichments by ideals and automorphisms, and the properties of the automorphism groups.