Download or read book The Covering Property Axiom CPA written by Krzysztof Ciesielski and published by Cambridge University Press. This book was released on 2004-08-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here the authors formulate and explore a new axiom of set theory, CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms, indeed it is true in the iterated Sacks model and actually captures the combinatorial core of this model. A plethora of results known to be true in the Sacks model easily follow from CPA. Replacing iterated forcing arguments with deductions from CPA simplifies proofs, provides deeper insight, and leads to new results. One may say that CPA is similar in nature to Martin's axiom, as both capture the essence of the models of ZFC in which they hold. The exposition is self contained and there are natural applications to real analysis and topology. Researchers who use set theory in their work will find much of interest in this book.
Download or read book The Covering Property Axiom CPA written by Krzysztof Ciesielski and published by . This book was released on 2004 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classical and New Paradigms of Computation and their Complexity Hierarchies written by Benedikt Löwe and published by Springer Science & Business Media. This book was released on 2007-11-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies. This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.
Download or read book The Covering Property Axiom CPA written by Krzysztof Ciesielski and published by Cambridge University Press. This book was released on 2004-08-23 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores a new axiom of set theory--CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms. It is true in the iterated Sacks model and actually captures the combinatorial core of this model. A plethora of results known to be true in the Sacks model easily follow from CPA. Replacing iterated forcing arguments with deductions from CPAs simplifies proofs, provides deeper insight, and leads to new results. Researchers who use set theory in their work will find much of interest in this book.
Download or read book Absolute Measurable Spaces written by Togo Nishiura and published by Cambridge University Press. This book was released on 2008-05-08 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes topological, geometrical and analytical properties of absolute measurable spaces; of interest for real analysis, set theory and measure theory.
Download or read book Centenary of the Borel Conjecture written by Marion Scheepers and published by American Mathematical Soc.. This book was released on 2020-09-04 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Borel's Conjecture entered the mathematics arena in 1919 as an innocuous remark about sets of real numbers in the context of a new covering property introduced by Émile Borel. In the 100 years since, this conjecture has led to a remarkably rich adventure of discovery in mathematics, producing independent results and the discovery of countable support iterated forcing, developments in infinitary game theory, deep connections with infinitary Ramsey Theory, and significant impact on the study of topological groups and topological covering properties. The papers in this volume present a broad introduction to the frontiers of research that has been spurred on by Borel's 1919 conjecture and identify fundamental unanswered research problems in the field. Philosophers of science and historians of mathematics can glean from this collection some of the typical trends in the discovery, innovation, and development of mathematical theories.
Download or read book Lineability written by Richard M. Aron and published by CRC Press. This book was released on 2015-10-05 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Renewed interest in vector spaces and linear algebras has spurred the search for large algebraic structures composed of mathematical objects with special properties. Bringing together research that was otherwise scattered throughout the literature, Lineability: The Search for Linearity in Mathematics collects the main results on the conditions for
Download or read book Forcing Idealized written by Jindrich Zapletal and published by Cambridge University Press. This book was released on 2008-02-07 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive set theory and definable proper forcing are two areas of set theory that developed quite independently of each other. This monograph unites them and explores the connections between them. Forcing is presented in terms of quotient algebras of various natural sigma-ideals on Polish spaces, and forcing properties in terms of Fubini-style properties or in terms of determined infinite games on Boolean algebras. Many examples of forcing notions appear, some newly isolated from measure theory, dynamical systems, and other fields. The descriptive set theoretic analysis of operations on forcings opens the door to applications of the theory: absoluteness theorems for certain classical forcing extensions, duality theorems, and preservation theorems for the countable support iteration. Containing original research, this text highlights the connections that forcing makes with other areas of mathematics, and is essential reading for academic researchers and graduate students in set theory, abstract analysis and measure theory.
Download or read book Modern Approaches to the Invariant Subspace Problem written by Isabelle Chalendar and published by Cambridge University Press. This book was released on 2011-08-18 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.
Download or read book Malliavin Calculus for L vy Processes and Infinite Dimensional Brownian Motion written by Horst Osswald and published by Cambridge University Press. This book was released on 2012-03 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.
Download or read book Rigidity in Higher Rank Abelian Group Actions Volume 1 Introduction and Cocycle Problem written by Anatole Katok and published by Cambridge University Press. This book was released on 2011-06-16 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems.
Download or read book Jordan Structures in Geometry and Analysis written by Cho-Ho Chu and published by Cambridge University Press. This book was released on 2011-11-17 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jordan theory has developed rapidly in the last three decades, but very few books describe its diverse applications. Here, the author discusses some recent advances of Jordan theory in differential geometry, complex and functional analysis, with the aid of numerous examples and concise historical notes. These include: the connection between Jordan and Lie theory via the Tits–Kantor–Koecher construction of Lie algebras; a Jordan algebraic approach to infinite dimensional symmetric manifolds including Riemannian symmetric spaces; the one-to-one correspondence between bounded symmetric domains and JB*-triples; and applications of Jordan methods in complex function theory. The basic structures and some functional analytic properties of JB*-triples are also discussed. The book is a convenient reference for experts in complex geometry or functional analysis, as well as an introduction to these areas for beginning researchers. The recent applications of Jordan theory discussed in the book should also appeal to algebraists.
Download or read book Polynomials and Vanishing Cycles written by Mihai Tibăr and published by Cambridge University Press. This book was released on 2007-05-17 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic geometro-topological approach to vanishing cycles appearing in non-proper fibrations is proposed in this tract. Lefschetz theory, complex Morse theory and singularities of hypersurfaces are presented in detail leading to the latest research on topics such as the topology of singularities of meromorphic functions and non-generic Lefschetz pencils.
Download or read book Convexity written by Barry Simon and published by Cambridge University Press. This book was released on 2011-05-19 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.
Download or read book Distribution Modulo One and Diophantine Approximation written by Yann Bugeaud and published by Cambridge University Press. This book was released on 2012-07-05 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, much of it from the last decade. There are numerous exercises to aid student understanding of the topic, and researchers will appreciate the notes at the end of each chapter, extensive references and open problems.
Download or read book The Theory of Hardy s Z Function written by A. Ivić and published by Cambridge University Press. This book was released on 2013 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of Hardy's Z-function, one of the most important functions of analytic number theory.
Download or read book Nonlinear Perron Frobenius Theory written by Bas Lemmens and published by Cambridge University Press. This book was released on 2012-05-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems.
