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Author : Deirdre Haskell,Ehud Hrushovski,Dugald Macpherson
Publisher : Cambridge University Press
Page : 189 pages
File Size : 55,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9780521889810
This book presents research in model theory and its applications to valued fields.
Author : Costas Dimitracopoulos
Publisher : Cambridge University Press
Page : 289 pages
File Size : 44,8 Mb
Release : 2008
Category : Logic, Symbolic and mathematical
ISBN : 9780521884259
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 : Lou van den Dries,Jochen Koenigsmann,H. Dugald Macpherson,Anand Pillay,Carlo Toffalori,Alex J. Wilkie
Publisher : Springer
Page : 201 pages
File Size : 48,8 Mb
Release : 2014-09-20
Category : Mathematics
ISBN : 9783642549366
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 : Ehud Hrushovski,François Loeser
Publisher : Princeton University Press
Page : 227 pages
File Size : 44,7 Mb
Release : 2016-02-09
Category : Mathematics
ISBN : 9781400881222
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 : Pierre Simon
Publisher : Cambridge University Press
Page : 165 pages
File Size : 55,9 Mb
Release : 2015-07-16
Category : Mathematics
ISBN : 9781107057753
The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.
Author : André C. M. Ran,H. J. J. te Riele,Jan Wiegerinck
Publisher : European Mathematical Society
Page : 496 pages
File Size : 41,9 Mb
Release : 2010
Category : Mathematics
ISBN : 3037190779
The European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000), and Stockholm (2004), the Fifth European Congress of Mathematics (5ECM) took place in Amsterdam, The Netherlands, July 14-18, 2008, with about 1000 participants from 68 different countries. Ten plenary and thirty-three invited lectures were delivered. Three science lectures outlined applications of mathematics in other sciences: climate change, quantum information theory, and population dynamics. As in the four preceding EMS congresses, ten EMS prizes were granted to very promising young mathematicians. In addition, the Felix Klein Prize was awarded, for the second time, for an application of mathematics to a concrete and difficult industrial problem. There were twenty-two minisymposia, spread over the whole mathematical area. Two round table meetings were organized: one on industrial mathematics and one on mathematics and developing countries. As part of the 44th Nederlands Mathematisch Congres, which was embedded in 5ECM, the so-called Brouwer lecture was presented. It is the Netherlands' most prestigious award in mathematics, organized every three years by the Royal Dutch Mathematical Society. Information about Brouwer was given in an invited historical lecture during the congress. These proceedings contain a selection of the contributions to the congress, providing a permanent record of the best of what mathematics offers today.
Author : Raf Cluckers,Johannes Nicaise,Julien Sebag
Publisher : Cambridge University Press
Page : 263 pages
File Size : 49,9 Mb
Release : 2011-09-22
Category : Mathematics
ISBN : 9781139501736
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.
Author : Matthew Baker,Sam Payne
Publisher : Springer
Page : 526 pages
File Size : 53,9 Mb
Release : 2016-08-18
Category : Mathematics
ISBN : 9783319309453
This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia. Topics covered in this volume include: Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons; The homotopy types of nonarchimedean analytifications; The existence of "faithful tropicalizations" which encode the topology and geometry of analytifications; Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves; Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory.
Author : Katrin Tent,Martin Ziegler
Publisher : Cambridge University Press
Page : 259 pages
File Size : 55,7 Mb
Release : 2012-03-08
Category : Mathematics
ISBN : 9780521763240
Concise introduction to current topics in model theory, including simple and stable theories.
Author : John T. Baldwin
Publisher : Cambridge University Press
Page : 365 pages
File Size : 44,6 Mb
Release : 2018-01-25
Category : Mathematics
ISBN : 9781107189218
Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.
Author : Jonathan Kirby
Publisher : Cambridge University Press
Page : 197 pages
File Size : 54,9 Mb
Release : 2019-04-18
Category : Mathematics
ISBN : 9781107163881
An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.
Author : Joseph Doyle Flenner
Publisher : Unknown
Page : 136 pages
File Size : 50,7 Mb
Release : 2008
Category : Electronic
ISBN : UCAL:C3486293
Author : Luc Bélair
Publisher : Unknown
Page : 496 pages
File Size : 46,5 Mb
Release : 2002
Category : Mathematics
ISBN : UOM:39015061016138
Author : Anonim
Publisher : Unknown
Page : 840 pages
File Size : 46,7 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015078588582
Author : Olga Kharlampovich,Rizos Sklinos
Publisher : Walter de Gruyter GmbH & Co KG
Page : 244 pages
File Size : 48,9 Mb
Release : 2021-05-10
Category : Mathematics
ISBN : 9783110719710
This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory. The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .