Author: Alfred Tarski
Publisher:
ISBN:
Category : Algebra, Abstract
Languages : en
Pages : 344
Book Description
Cardinal Algebras
Author: Alfred Tarski
Publisher:
ISBN:
Category : Algebra, Abstract
Languages : en
Pages : 344
Book Description
Publisher:
ISBN:
Category : Algebra, Abstract
Languages : en
Pages : 344
Book Description
Cardinal Invariants on Boolean Algebras
Author: J. Donald Monk
Publisher: 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.
Publisher: 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.
Cardinal Functions on Boolean Algebras
Author: MONK
Publisher: Birkhäuser
ISBN: 3034863810
Category : Science
Languages : en
Pages : 159
Book Description
Publisher: Birkhäuser
ISBN: 3034863810
Category : Science
Languages : en
Pages : 159
Book Description
Cardinal Algebras
Author: Alfred Tarski
Publisher:
ISBN:
Category : Algebra, Abstract
Languages : en
Pages : 352
Book Description
Publisher:
ISBN:
Category : Algebra, Abstract
Languages : en
Pages : 352
Book Description
Cardinal Invariants on Boolean Algebras
Author: J. Donald Monk
Publisher: Springer Science & Business Media
ISBN: 3034807309
Category : Mathematics
Languages : en
Pages : 569
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.
Publisher: Springer Science & Business Media
ISBN: 3034807309
Category : Mathematics
Languages : en
Pages : 569
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.
The Application of Cardinal Algebras to the Dimension Theory of Operator Algebras
Author: Peter A. Fillmore
Publisher:
ISBN:
Category : Algebra, Abstract
Languages : en
Pages : 140
Book Description
Publisher:
ISBN:
Category : Algebra, Abstract
Languages : en
Pages : 140
Book Description
Cardinal Functions on Boolean Algebras
Author: James Donald Monk
Publisher: Birkhauser
ISBN:
Category : Mathematics
Languages : en
Pages : 172
Book Description
Publisher: Birkhauser
ISBN:
Category : Mathematics
Languages : en
Pages : 172
Book Description
Cardinal Algebras
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 326
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 326
Book Description
Boolean Algebras
Author: Roman Sikorski
Publisher: Springer
ISBN: 3662015072
Category : Mathematics
Languages : en
Pages : 245
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 [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.
Publisher: Springer
ISBN: 3662015072
Category : Mathematics
Languages : en
Pages : 245
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 [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.
Measure Theory
Author: D. H. Fremlin
Publisher: Torres Fremlin
ISBN: 0953812936
Category : Fourier analysis
Languages : en
Pages : 693
Book Description
Publisher: Torres Fremlin
ISBN: 0953812936
Category : Fourier analysis
Languages : en
Pages : 693
Book Description