Cardinal Algebras
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Cardinal Algebras
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Author : Alfred Tarski
language : en
Publisher:
Release Date : 1949
Cardinal Algebras written by Alfred Tarski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1949 with Algebra, Abstract categories.
Cardinal Invariants On Boolean Algebras
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Author : J. Donald Monk
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-11
Cardinal Invariants On Boolean Algebras written by J. Donald Monk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-11 with Mathematics categories.
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.
Cardinal Invariants On Boolean Algebras
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Author : J. Donald Monk
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-25
Cardinal Invariants On Boolean Algebras written by J. Donald Monk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-25 with Mathematics categories.
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
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Author : James Donald Monk
language : en
Publisher: Birkhauser
Release Date : 1990
Cardinal Functions On Boolean Algebras written by James Donald Monk and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
The Application Of Cardinal Algebras To The Dimension Theory Of Operator Algebras
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Author : Peter A. Fillmore
language : en
Publisher:
Release Date : 1962
The Application Of Cardinal Algebras To The Dimension Theory Of Operator Algebras written by Peter A. Fillmore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Algebra, Abstract categories.
Cardinal Invariants On Boolean Algebras
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Author : James Donald Monk
language : en
Publisher: Birkhauser
Release Date : 1996
Cardinal Invariants On Boolean Algebras written by James Donald Monk and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Cardinal Functions On Boolean Algebras
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Author : MONK
language : en
Publisher: Birkhäuser
Release Date : 2013-12-14
Cardinal Functions On Boolean Algebras written by MONK and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-14 with Science categories.
Cardinal Invariants On Boolean Algebras
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Author : James Donald Monk
language : en
Publisher: Springer Science & Business Media
Release Date : 1996
Cardinal Invariants On Boolean Algebras written by James Donald Monk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
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 to 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 97 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) by the same author, the present work is nearly twice the size of the original work. It contains solutions to many of the open problems which are discussed in greater detail than before. Among the new topics considered are ultraproducts and FedorchukA-s theorem, and there is a more complete treatment of the cellularity of free products. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including tree algebras and superatomic algebras. Review: "This book is an indispensable tool for anyone working in Boolean algebra, and is also recommended for set-theoretic topologists." - Zentralblatt MATH
Boolean Algebras
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Author : Roman Sikorski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Boolean Algebras written by Roman Sikorski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Introduction To The Theory Of Abstract Algebras
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Author : Richard S Pierce
language : en
Publisher: Courier Corporation
Release Date : 2015-01-21
Introduction To The Theory Of Abstract Algebras written by Richard S Pierce and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-21 with Mathematics categories.
"Suitable for introductory graduate-level courses and independent study, this text presents the basic definitions of the theory of abstract algebra. Following introductory material, each of four chapters focuses on a major theme of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebra. Problems and a bibliography supplement the text. "--