Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Descriptive Set Theory And Definable Forcing
Download Descriptive Set Theory And Definable Forcing full books in PDF, epub, and Kindle. Read online Descriptive Set Theory And Definable Forcing ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Descriptive Set Theory and Definable Forcing by : Jindřich Zapletal
Download or read book Descriptive Set Theory and Definable Forcing written by Jindřich Zapletal and published by American Mathematical Soc.. This book was released on 2004 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on the relationship between definable forcing and descriptive set theory; the forcing serves as a tool for proving independence of inequalities between cardinal invariants of the continuum.
Book Synopsis Descriptive Set Theory and Forcing by : Arnold W. Miller
Download or read book Descriptive Set Theory and Forcing written by Arnold W. Miller and published by Cambridge University Press. This book was released on 2017-05-18 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourth publication in the Lecture Notes in Logic series, Miller develops the necessary features of the theory of descriptive sets in order to present a new proof of Louveau's separation theorem for analytic sets. While some background in mathematical logic and set theory is assumed, the material is based on a graduate course given by the author at the University of Wisconsin, Madison, and is thus accessible to students and researchers alike in these areas, as well as in mathematical analysis.
Book Synopsis Forcing Idealized by : Jindřich Zapletal
Download or read book Forcing Idealized written by Jindřich Zapletal and published by . This book was released on 2014-05-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unites descriptive set theory and definable proper forcing and explores the relations between them. Both forcing and descriptive set theory are explained independently, their sub-areas described, following their commitment to each other. This text highlights the connections that forcing makes with other areas of mathematics, such as set theory, abstract analysis, and measure theory.--From publisher description.
Book Synopsis Forcing Idealized by : Jindrich Zapletal
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.
Book Synopsis Classical Descriptive Set Theory by : Alexander Kechris
Download or read book Classical Descriptive Set Theory written by Alexander Kechris and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.
Book Synopsis Handbook of Set Theory by : Matthew Foreman
Download or read book Handbook of Set Theory written by Matthew Foreman and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 2230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
Download or read book Set Theory written by Ralf Schindler and published by Springer. This book was released on 2014-05-22 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing and descriptive set theory. The following topics are covered: • Forcing and constructability • The Solovay-Shelah Theorem i.e. the equiconsistency of ‘every set of reals is Lebesgue measurable’ with one inaccessible cardinal • Fine structure theory and a modern approach to sharps • Jensen’s Covering Lemma • The equivalence of analytic determinacy with sharps • The theory of extenders and iteration trees • A proof of projective determinacy from Woodin cardinals. Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers.
Book Synopsis Canonical Ramsey Theory on Polish Spaces by : Vladimir Kanovei
Download or read book Canonical Ramsey Theory on Polish Spaces written by Vladimir Kanovei and published by Cambridge University Press. This book was released on 2013-09-12 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lays the foundations for a new area of descriptive set theory: the connection between forcing and analytic equivalence relations.
Book Synopsis Borel Equivalence Relations by : Vladimir Grigorʹevich Kanoveĭ
Download or read book Borel Equivalence Relations written by Vladimir Grigorʹevich Kanoveĭ and published by American Mathematical Soc.. This book was released on 2008 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The book presents, for the first time in mathematical literature, all major aspects of this theory and its applications."--BOOK JACKET.
Download or read book Advances in Logic written by Su Gao and published by American Mathematical Soc.. This book was released on 2007 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book are based on talks given at the North Texas Logic Conference in October of 2004. The main goal of the editors was to collect articles representing diverse fields within logic that would both contain significant new results and be accessible to readers with a general background in logic. Included in the book is a problem list, jointly compiled by the speakers, that reflects some of the most important questions in various areas of logic. This book should be useful to graduate students and researchers alike across the spectrum of mathematical logic.
Book Synopsis The Covering Property Axiom, CPA by : Krzysztof Ciesielski
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.
Book Synopsis Measure Theoretic Laws for lim sup Sets by : Victor Beresnevich
Download or read book Measure Theoretic Laws for lim sup Sets written by Victor Beresnevich and published by American Mathematical Soc.. This book was released on 2006 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a compact metric space $(\Omega,d)$ equipped with a non-atomic, probability measure $m$ and a positive decreasing function $\psi$, we consider a natural class of lim sup subsets $\Lambda(\psi)$ of $\Omega$. The classical lim sup set $W(\psi)$ of `$\p$-approximable' numbers in the theory of metric Diophantine approximation fall within this class. We establish sufficient conditions (which are also necessary under some natural assumptions) for the $m$-measure of $\Lambda(\psi)$to be either positive or full in $\Omega$ and for the Hausdorff $f$-measure to be infinite. The classical theorems of Khintchine-Groshev and Jarník concerning $W(\psi)$ fall into our general framework. The main results provide a unifying treatment of numerous problems in metric Diophantineapproximation including those for real, complex and $p$-adic fields associated with both independent and dependent quantities. Applications also include those to Kleinian groups and rational maps. Compared to previous works our framework allows us to successfully remove many unnecessary conditions and strengthen fundamental results such as Jarník's theorem and the Baker-Schmidt theorem. In particular, the strengthening of Jarník's theorem opens up the Duffin-Schaeffer conjecturefor Hausdorff measures.
Book Synopsis Measure Theoretic Laws for lim sup Sets by : Victor Beresnevich Detta Dickinson Sanju Velani
Download or read book Measure Theoretic Laws for lim sup Sets written by Victor Beresnevich Detta Dickinson Sanju Velani and published by American Mathematical Soc.. This book was released on 2005-12-01 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a compact metric space $(\Omega,d)$ equipped with a non-atomic, probability measure $m$ and a positive decreasing function $\psi$, we consider a natural class of lim sup subsets $\Lambda(\psi)$ of $\Omega$. The classical lim sup set $W(\psi)$ of `$\psi$-approximable' numbers in the theory of metric Diophantine approximation fall within this class. We establish sufficient conditions (which are also necessary under some natural assumptions) for the $m$-measure of $\Lambda(\psi)$ to be either positive or full in $\Omega$ and for the Hausdorff $f$-measure to be infinite. The classical theorems of Khintchine-Groshev and Jarnik concerning $W(\psi)$ fall into our general framework. The main results provide a unifying treatment of numerous problems in metric Diophantine approximation including those for real, complex and $p$-adic fields associated with both independent and dependent quantities. Applications also include those to Kleinian groups and rational maps. Compared to previous works our framework allows us to successfully remove many unnecessary conditions and strengthen fundamental results such as Jarnik's theorem and the Baker-Schmidt theorem. In particular, the strengthening of Jarnik's theorem opens up the Duffin-Schaeffer conjecture for Hausdorff measures.
Book Synopsis Descriptive Set Theory and Forcing by : Arnold Miller
Download or read book Descriptive Set Theory and Forcing written by Arnold Miller and published by Springer. This book was released on 1995-09-18 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate course assumes some knowledge of forcing as well as some elementary mathematical logic, e.g. the Lowenheim-Skolem Theorem. The first half deals with the general area of Borel hierarchies, probing lines of enquiry such as the possible lengths of a Borel hierarchy in a separable metric space. The second half goes on to include Harrington's Theorem together with a proof and applications of Louveau's Theorem on hyperprojective parameters.
Book Synopsis Classical and New Paradigms of Computation and their Complexity Hierarchies by : Benedikt Löwe
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.
Book Synopsis An Analogue of a Reductive Algebraic Monoid Whose Unit Group Is a Kac-Moody Group by : Claus Mokler
Download or read book An Analogue of a Reductive Algebraic Monoid Whose Unit Group Is a Kac-Moody Group written by Claus Mokler and published by American Mathematical Soc.. This book was released on 2005 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: By an easy generalization of the Tannaka-Krein reconstruction we associate to the category of admissible representations of the category ${\mathcal O}$ of a Kac-Moody algebra, and its category of admissible duals, a monoid with a coordinate ring. The Kac-Moody group is the Zariski open dense unit group of this monoid. The restriction of the coordinate ring to the Kac-Moody group is the algebra of strongly regular functions introduced by V. Kac and D. Peterson. This monoid has similar structural properties as a reductive algebraic monoid. In particular it is unit regular, its idempotents related to the faces of the Tits cone. It has Bruhat and Birkhoff decompositions. The Kac-Moody algebra is isomorphic to the Lie algebra of this monoid.
Book Synopsis The Complex Monge-Ampere Equation and Pluripotential Theory by : Sławomir Kołodziej
Download or read book The Complex Monge-Ampere Equation and Pluripotential Theory written by Sławomir Kołodziej and published by American Mathematical Soc.. This book was released on 2005 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: We collect here results on the existence and stability of weak solutions of complex Monge-Ampere equation proved by applying pluripotential theory methods and obtained in past three decades. First we set the stage introducing basic concepts and theorems of pluripotential theory. Then the Dirichlet problem for the complex Monge-Ampere equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part, the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampere equation on compact Kahler manifolds. This is a generalization of the Calabi-Yau theorem.
