Descriptive Set Theory And Definable Forcing

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Descriptive Set Theory And Definable Forcing

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Author : Jindřich Zapletal
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Descriptive Set Theory And Definable Forcing written by Jindřich Zapletal and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

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.

Forcing For Mathematicians

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Author : Nik Weaver
language : en
Publisher: World Scientific
Release Date : 2014-01-24

Forcing For Mathematicians written by Nik Weaver and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-24 with Mathematics categories.

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.

Handbook Of Set Theory

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Author : Matthew Foreman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-10

Handbook Of Set Theory written by Matthew Foreman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-10 with Mathematics categories.

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.

The Axiom Of Determinacy Forcing Axioms And The Nonstationary Ideal

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Author : W. Hugh Woodin
language : en
Publisher: Walter de Gruyter
Release Date : 2013-02-01

The Axiom Of Determinacy Forcing Axioms And The Nonstationary Ideal written by W. Hugh Woodin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-01 with Mathematics categories.

The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

On Dynamical Poisson Groupoids I

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Author : Luen-Chau Li
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

On Dynamical Poisson Groupoids I written by Luen-Chau Li and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

We address the question of duality for the dynamical Poisson groupoids of Etingof and Varchenko over a contractible base. We also give an explicit description for the coboundary case associated with the solutions of (CDYBE) on simple Lie algebras as classified by the same authors.

Maximum Principles On Riemannian Manifolds And Applications

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Author : Stefano Pigola
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Maximum Principles On Riemannian Manifolds And Applications written by Stefano Pigola and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.

A Generating Function Approach To The Enumeration Of Matrices In Classical Groups Over Finite Fields

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Author : Jason Fulman
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

A Generating Function Approach To The Enumeration Of Matrices In Classical Groups Over Finite Fields written by Jason Fulman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

Generating function techniques are used to study the probability that an element of a classical group defined over a finite field is separable, cyclic, semisimple or regular. The limits of these probabilities as the dimension tends to infinity are calculated in all cases, and exponential convergence to the limit is proved. These results complement and extend earlier results of the authors, G. E. Wall, and Guralnick & Lubeck.

Generative Complexity In Algebra

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Author : Joel Berman
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Generative Complexity In Algebra written by Joel Berman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

Considers the behavior of $\mathrm{G}_\mathcal{C}(k)$ when $\mathcal{C}$ is a locally finite equational class (variety) of algebras and $k$ is finite. This title looks at ways that algebraic properties of $\mathcal{C}$ lead to upper or lower bounds on generative complexity.

Large Viscous Boundary Layers For Noncharacteristic Nonlinear Hyperbolic Problems

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Author : Guy Métivier
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Large Viscous Boundary Layers For Noncharacteristic Nonlinear Hyperbolic Problems written by Guy Métivier and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

Studies two types of integral transformation associated with fractional Brownian motion, that are applied to construct approximation schemes for fractional Brownian motion by polygonal approximation of standard Brownian motion. This approximation is the best in the sense that it minimizes the mean square error.

Entropy Bounds And Isoperimetry

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Author : Serguei Germanovich Bobkov
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Entropy Bounds And Isoperimetry written by Serguei Germanovich Bobkov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.

In these memoirs Bobkov and Zegarlinski describe interesting developments in infinite dimensional analysis that moved it away from experimental science. Here they also describe Poincar -type inequalities, entropy and Orlicz spaces, LSq and Hardy-type inequalities on the line, probability measures satisfying LSq inequalities on the real line, expo