Author: Deirdre Haskell
Publisher: Cambridge University Press
ISBN: 0521889812
Category : Mathematics
Languages : en
Pages : 189

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Book Description
This book presents research in model theory and its applications to valued fields.

Author: Antonio J. Engler
Publisher: Springer Science & Business Media
ISBN: 354030035X
Category : Mathematics
Languages : en
Pages : 210

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Book Description
Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.

Author: Pierre Simon
Publisher: Cambridge University Press
ISBN: 1107057752
Category : Mathematics
Languages : en
Pages : 165

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Book Description
The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.

Author: Ehud Hrushovski
Publisher: Princeton University Press
ISBN: 0691161690
Category : Mathematics
Languages : en
Pages : 226

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Book Description
Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on the set of complex points, and it has become an important tool in algebraic dynamics and many other areas of geometry. This book lays down model-theoretic foundations for non-archimedean geometry. The methods combine o-minimality and stability theory. Definable types play a central role, serving first to define the notion of a point and then properties such as definable compactness. Beyond the foundations, the main theorem constructs a deformation retraction from the full non-archimedean space of an algebraic variety to a rational polytope. This generalizes previous results of V. Berkovich, who used resolution of singularities methods. No previous knowledge of non-archimedean geometry is assumed. Model-theoretic prerequisites are reviewed in the first sections.

Author: Costas Dimitracopoulos
Publisher: Cambridge University Press
ISBN: 052188425X
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 289

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Book Description
The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of developments, and the rest of the papers are chosen to complement the invited talks. This 2007 volume includes surveys, tutorials, and selected research papers from the 2005 meeting. Highlights include three papers on different aspects of connections between model theory and algebra; a survey of major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.

Author: victor ginzburg
Publisher: Springer Science & Business Media
ISBN: 0817645322
Category : Mathematics
Languages : en
Pages : 656

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Book Description
This book represents a collection of invited papers by outstanding mathematicians in algebra, algebraic geometry, and number theory dedicated to Vladimir Drinfeld. Original research articles reflect the range of Drinfeld's work, and his profound contributions to the Langlands program, quantum groups, and mathematical physics are paid particular attention. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory.

Author: Jose Iovino
Publisher: CRC Press
ISBN: 1498754015
Category : Mathematics
Languages : en
Pages : 427

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Book Description
Model theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.

Author: Craig Huneke
Publisher: Cambridge University Press
ISBN: 0521688604
Category : Mathematics
Languages : en
Pages : 446

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Book Description
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

Author: Lou van den Dries
Publisher: Springer
ISBN: 3642549365
Category : Mathematics
Languages : en
Pages : 201

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Book Description
Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.

Author:
Publisher:
ISBN:
Category : Philosophy
Languages : en
Pages : 1376

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Book Description
Vols. for 1969- include a section of abstracts.