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Author : Alfred Tarski,Bjarni Jónsson
Publisher : Unknown
Page : 352 pages
File Size : 49,6 Mb
Release : 1949
Category : Algebra, Abstract
ISBN : UOM:39015011444703
Author : J. Donald Monk
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 40,5 Mb
Release : 2014-02-11
Category : Mathematics
ISBN : 9783034807302
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.
Author : James Donald Monk
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 46,7 Mb
Release : 1996
Category : Mathematics
ISBN : 376435402X
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
Author : MONK
Publisher : Birkhäuser
Page : 159 pages
File Size : 54,7 Mb
Release : 2013-12-14
Category : Science
ISBN : 9783034863810
Author : J. Donald Monk
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 47,7 Mb
Release : 2010-03-25
Category : Mathematics
ISBN : 9783034603348
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.
Author : James Donald Monk
Publisher : Birkhauser
Page : 168 pages
File Size : 40,9 Mb
Release : 1990
Category : Mathematics
ISBN : UCAL:B4342387
Author : Peter A. Fillmore
Publisher : Unknown
Page : 140 pages
File Size : 54,9 Mb
Release : 1962
Category : Algebra, Abstract
ISBN : MINN:31951T00402742T
Author : Friedrich Wehrung
Publisher : Springer
Page : 242 pages
File Size : 45,9 Mb
Release : 2017-09-09
Category : Mathematics
ISBN : 9783319615998
Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.
Author : Susan J. Andima
Publisher : CRC Press
Page : 440 pages
File Size : 53,9 Mb
Release : 2020-08-26
Category : Mathematics
ISBN : 9781000147872
This book is based on the proceedings of the Fifth Northeast Conference on General Topology and Applications, held at The College of Staten Island – The City University of New York. It provides insight into the relationship between general topology and other areas of mathematics.
Author : Lev D. Beklemishev
Publisher : Elsevier
Page : 132 pages
File Size : 51,5 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080957390
Provability, Computability and Reflection
Author : P. Burmeister
Publisher : Walter de Gruyter GmbH & Co KG
Page : 324 pages
File Size : 51,6 Mb
Release : 1986-12-31
Category : Mathematics
ISBN : 9783112720875
No detailed description available for "A Model Theoretic Oriented Approach to Partial Algebras".
Author : Ilijas Farah
Publisher : Springer Nature
Page : 517 pages
File Size : 40,7 Mb
Release : 2019-12-24
Category : Mathematics
ISBN : 9783030270933
This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.
Author : A. G. Kurosh
Publisher : Elsevier
Page : 375 pages
File Size : 53,8 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483149578
Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.
Author : S. N. Cernikov,N. V. Cernikova,A. N. Kolmogorov,A. I. Mal'cev,B. I. Plotkin
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 46,5 Mb
Release : 1961-12-31
Category : Electronic
ISBN : 0821817175
Author : Steven Givant,Paul Halmos
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 51,7 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9780387684369
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.