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Ordinal Algebras
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Book Synopsis Cardinal Invariants on Boolean Algebras by : J. Donald Monk
Download or read book Cardinal Invariants on Boolean Algebras written by J. Donald Monk and published by Springer Science & Business Media. This book was released on 2014-02-11 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Cardinal Functions on Boolean Algebras by : MONK
Download or read book Cardinal Functions on Boolean Algebras written by MONK and published by Birkhäuser. This book was released on 2013-12-14 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cardinal Invariants On Boolean Algebras by : James Donald Monk
Download or read book Cardinal Invariants On Boolean Algebras written by James Donald Monk and published by Springer Science & Business Media. This book was released on 1996 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Countable Boolean Algebras and Decidability by : Sergey Goncharov
Download or read book Countable Boolean Algebras and Decidability written by Sergey Goncharov and published by Springer Science & Business Media. This book was released on 1997-01-31 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Representations of Algebras by : Graham J. Leuschke
Download or read book Representations of Algebras written by Graham J. Leuschke and published by American Mathematical Soc.. This book was released on 2018 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held in August 2016, at Syracuse University. This volume includes three survey articles based on short courses in the areas of commutative algebraic groups, modular group representation theory, and thick tensor ideals of bounded derived categories.
Book Synopsis Cardinal Algebras by : Alfred Tarski
Download or read book Cardinal Algebras written by Alfred Tarski and published by . This book was released on 1949 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Automata and Algebras in Categories by : Jirí Adámek
Download or read book Automata and Algebras in Categories written by Jirí Adámek and published by Springer Science & Business Media. This book was released on 1990-08-31 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monograph( based very largely upon results original to the Czechoslovakian authors) presents an abstract account of the theory of automata for sophisticated readers presumed to be already conversant in the language of category theory. The seven chapters are punctuated at frequent intervals by exampl
Book Synopsis Provability, Computability and Reflection by : Lev D. Beklemishev
Download or read book Provability, Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection
Book Synopsis Boolean Constructions in Universal Algebras by : A.G. Pinus
Download or read book Boolean Constructions in Universal Algebras written by A.G. Pinus and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last few decades the ideas, methods, and results of the theory of Boolean algebras have played an increasing role in various branches of mathematics and cybernetics. This monograph is devoted to the fundamentals of the theory of Boolean constructions in universal algebra. Also considered are the problems of presenting different varieties of universal algebra with these constructions, and applications for investigating the spectra and skeletons of varieties of universal algebras. For researchers whose work involves universal algebra and logic.
Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Boolean Algebras by : Steven Givant
Download or read book Introduction to Boolean Algebras written by Steven Givant and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fundamental Structures of Algebra and Discrete Mathematics by : Stephan Foldes
Download or read book Fundamental Structures of Algebra and Discrete Mathematics written by Stephan Foldes and published by John Wiley & Sons. This book was released on 2011-02-14 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.
Book Synopsis Open Problems in Topology II by : Elliott M. Pearl
Download or read book Open Problems in Topology II written by Elliott M. Pearl and published by Elsevier. This book was released on 2011-08-11 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis.* New surveys of research problems in topology* New perspectives on classic problems* Representative surveys of research groups from all around the world
Book Synopsis Lectures on Soft Computing and Fuzzy Logic by : Antonio Di Nola
Download or read book Lectures on Soft Computing and Fuzzy Logic written by Antonio Di Nola and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume collects selected papers arising from lectures delivered by the authors at the School on Fuzzy Logic and Soft Computing held during the years 1996/97/98/99 and sponsored by the Salerno University. The authors contributing to this volume agreed with editors to write down, to enlarge and, in many cases, to rethink their original lectures, in order to offer to readership, a more compact presentation of the proposed topics. The aim of the volume is to offer a picture, as a job in progress, of the effort that is coming in founding and developing soft computing's techniques. The volume contains papers aimed to report on recent results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover algebraic aspects of Lukasiewicz Logic, Fuzzy Logic as the logic of continuous t-norms, Intuitionistic Fuzzy Logic. Aspects of fuzzy logic based on similar ity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present re sults in Probability Logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are presented in the book. Indeed we find applications ranging among pattern recognition, image and signal processing, evolutionary agents, fuzzy cellular networks, classi fication in fuzzy environments. The volume is then intended to serve as a reference work for foundational logico-algebraic aspect of Soft Computing and for concrete applications of soft computing technologies.
Book Synopsis Abstract Algebra by : Paul B. Garrett
Download or read book Abstract Algebra written by Paul B. Garrett and published by CRC Press. This book was released on 2007-09-25 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narra
Book Synopsis Probability Algebras and Stochastic Spaces by : Demetrios A. Kappos
Download or read book Probability Algebras and Stochastic Spaces written by Demetrios A. Kappos and published by Academic Press. This book was released on 2014-07-03 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability Algebras and Stochastic Spaces explores the fundamental notions of probability theory in the so-called "point-free way. The space of all elementary random variables defined over a probability algebra in a "point-free way is a base for the stochastic space of all random variables, which can be obtained from it by lattice-theoretic extension processes. This book is composed of eight chapters and begins with discussions of the definition, properties, scope, and extension of probability algebras. The succeeding chapters deal with the Cartesian product of probability algebras and the principles of stochastic spaces. These topics are followed by surveys of the expectation, moments, and spaces of random variables. The final chapters define generalized random variables and the Boolean homomorphisms of these variables. This book will be of great value to mathematicians and advance mathematics students.
Book Synopsis Alfred Tarski by : Anita Burdman Feferman
Download or read book Alfred Tarski written by Anita Burdman Feferman and published by Cambridge University Press. This book was released on 2004-10-04 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
