Canonical Ramsey Theory on Polish Spaces PDF Download
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Author: Vladimir Kanovei
Publisher: Cambridge University Press
ISBN: 1107026857
Category : Mathematics
Languages : en
Pages : 279
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Book Description
Lays the foundations for a new area of descriptive set theory: the connection between forcing and analytic equivalence relations.
Author: Vladimir Kanovei
Publisher: Cambridge University Press
ISBN: 1107026857
Category : Mathematics
Languages : en
Pages : 279
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Book Description
Lays the foundations for a new area of descriptive set theory: the connection between forcing and analytic equivalence relations.
Author: Paul B. Larson
Publisher: American Mathematical Soc.
ISBN: 1470454629
Category : Education
Languages : en
Pages : 345
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Book Description
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.
Author: D. E. Edmunds
Publisher: Cambridge University Press
ISBN: 1009254634
Category : Mathematics
Languages : en
Pages : 169
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Book Description
Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.
Author: Omar El-Fallah
Publisher: Cambridge University Press
ISBN: 1107047528
Category : Mathematics
Languages : en
Pages : 227
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Book Description
The first systematic account of the Dirichlet space, one of the most fundamental Hilbert spaces of analytic functions.
Author: Ralf Schindler
Publisher: Springer
ISBN: 3319067257
Category : Mathematics
Languages : en
Pages : 335
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Book Description
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.
Author: Jim Agler
Publisher: Cambridge University Press
ISBN: 1108618588
Category : Mathematics
Languages : en
Pages : 393
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Book Description
This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices.
Author: Joseph A. Ball
Publisher: Cambridge University Press
ISBN: 131651899X
Category : Mathematics
Languages : en
Pages : 439
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Book Description
This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.
Author: Chris Wendl
Publisher: Cambridge University Press
ISBN: 1108497403
Category : Mathematics
Languages : en
Pages : 197
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Book Description
An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.
Author: David Masser
Publisher: Cambridge University Press
ISBN: 1107061571
Category : Mathematics
Languages : en
Pages : 367
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Book Description
A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.
Author: Elizabeth S. Meckes
Publisher: Cambridge University Press
ISBN: 1108317995
Category : Mathematics
Languages : en
Pages : 225
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Book Description
This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.
