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.
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.
Download or read book Descriptive Set Theory and Forcing written by Arnold W. Miller and published by . This book was released on 2002-01-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is based on a graduate course given by the author at the University of Wisconsin. It presents an exposition of basic material from descriptive set theory (the general theory of Borel sets and projective sets), leading up to a new proof of Louveau's separation theorem for analytic sets. It assumes some background in mathematical logic and set theory, and should be of interest to reseachers and advanced students in these areas as well as in mathematical analysis. 4
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 Forcing Idealized written by Jindřich Zapletal and published by . This book was released on 2008 with total page 314 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.
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.
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.
Download or read book Forcing For Mathematicians written by Nik Weaver and published by World Scientific. This book was released on 2014-01-24 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics.
Download or read book Geometric Set Theory written by Paul B. Larson and published by American Mathematical Soc.. This book was released on 2020-07-16 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo–Fraenkel set theory without Axiom of Choice. The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.
Download or read book Descriptive Set Theory written by Y.N. Moschovakis and published by Elsevier. This book was released on 1987-01-01 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now available in paperback, this monograph is a self-contained exposition of the main results and methods of descriptive set theory. It develops all the necessary background material from logic and recursion theory, and treats both classical descriptive set theory and the effective theory developed by logicians.
Download or read book Set Theory An Introduction To Independence Proofs written by K. Kunen and published by Elsevier. This book was released on 2014-06-28 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.
Download or read book The Role of the Spectrum in the Cyclic Behavior of Composition Operators written by Eva A. Gallardo-Gutieŕrez and published by American Mathematical Soc.. This book was released on 2004 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction and preliminaries Linear fractional maps with an interior fixed point Non elliptic automorphisms The parabolic non automorphism Supercyclic linear fractional composition operators Endnotes Bibliography.
Download or read book Quasi Ordinary Power Series and Their Zeta Functions written by Enrique Artal-Bartolo and published by American Mathematical Soc.. This book was released on 2005-10-05 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic zeta function $Z_{\text{DL}}(h,T)$ of a quasi-ordinary power series $h$ of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities. This allows us to effectively represent $Z_{\text{DL}}(h,T)=P(T)/Q(T)$ such that almost all the candidate poles given by $Q(T)$ are poles. Anyway, these candidate poles give eigenvalues of the monodromy action on the complex $R\psi_h$ of nearby cycles on $h^{-1}(0).$ In particular we prove in this case the monodromy conjecture made by Denef-Loeser for the local motivic zeta function and the local topological zeta function. As a consequence, if $h$ is a quasi-ordinary polynomial defined over a number field we prove the Igusa monodromy conjecture for its local Igusa zeta function.
Download or read book Uniformizing Dessins and BelyiMaps via Circle Packing written by Philip L. Bowers and published by American Mathematical Soc.. This book was released on 2004 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction Dessins d'enfants Discrete Dessins via circle packing Uniformizing Dessins A menagerie of Dessins d'enfants Computational issues Additional constructions Non-equilateral triangulations The discrete option Appendix: Implementation Bibliography.
Download or read book A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring written by Ehud Friedgut and published by American Mathematical Soc.. This book was released on 2006 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $\cal{R}$ be the set of all finite graphs $G$ with the Ramsey property that every coloring of the edges of $G$ by two colors yields a monochromatic triangle. In this paper the authors establish a sharp threshold for random graphs with this property. Let $G(n, p)$ be the random graph on $n$ vertices with edge probability $p$. The authors prove that there exists a function $\widehat c=\widehat c(n)=\Theta(1)$ such that for any $\varepsilon > 0$, as $n$ tends to infinity, $Pr\left[G(n, (1-\varepsilon)\widehat c/\sqrt{n}) \in \cal{R} \right] \rightarrow 0$ and $Pr \left[ G(n, (1]\varepsilon)\widehat c/\sqrt{n}) \in \cal{R}\ \right] \rightarrow 1.$. A crucial tool that is used in the proof and is of independent interest is a generalization of Szemeredi's Regularity Lemma to a certain hypergraph setti
Download or read book Exceptional Vector Bundles Tilting Sheaves and Tilting Complexes for Weighted Projective Lines written by Hagen Meltzer and published by American Mathematical Soc.. This book was released on 2004 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with weighted projective lines, a class of non-commutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finite-dimensional algebras; the complexity of the classification of coherent sheaves largely depends on the genus of these curves.
Download or read book Kahler Spaces Nilpotent Orbits and Singular Reduction written by Johannes Huebschmann and published by American Mathematical Soc.. This book was released on 2004 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a stratified symplectic space, a suitable concept of stratified Kahler polarization encapsulates Kahler polarizations on the strata and the behaviour of the polarizations across the strata and leads to the notion of stratified Kahler space which establishes an intimate relationship between nilpotent orbits, singular reduction, invariant theory, reductive dual pairs, Jordan triple systems, symmetric domains, and pre-homogeneous spaces: The closure of a holomorphic nilpotent orbit or, equivalently, the closure of the stratum of the associated pre-homogeneous space of parabolic type carries a (positive) normal Kahler structure. In the world of singular Poisson geometry, the closures of principal holomorphic nilpotent orbits, positive definite hermitian JTS's, and certain pre-homogeneous spaces appear as different incarnations of the same structure. The closure of the principal holomorphic nilpotent orbit arises from a semisimple holomorphic orbit by contraction. Symplectic reduction carries a positive Kahler manifold to a positive normal Kahler space in such a way that the sheaf of germs of polarized functions coincides with the ordinary sheaf of germs of holomorphic functions. Symplectic reduction establishes a close relationship between singular reduced spaces and nilpotent orbits of the dual groups. Projectivization of holomorphic nilpotent orbits yields exotic (positive) stratified Kahler structures on complex projective spaces and on certain complex projective varieties including complex projective quadrics. The space of (in general twisted) representations of the fundamental group of a closed surface in a compact Lie group or, equivalently, a moduli space of central Yang-Mills connections on a principal bundle over a surface, inherits a (positive) normal (stratified) Kahler structure. Physical examples are provided by certain reduced spaces arising from angular momentum zero.
