Lecture notes on o-minimal structures and real analytic geometry / edited by Chris Miller, Jean-Philippe Rolin, Patrick Speissegger

Auteur secondaire : Miller, Christopher - Editeur scientifique ; Rolin, Jean-Philippe (1959-) - Editeur scientifique ; Speissegger, Patrick - Editeur scientifiqueType de document: MonographieCollection: Fields Institute communications ; 62Langue: anglaisPays: Etats UnisÉditeur: New York : Springer, 2012Description: 1 vol. (242 p.) ; 23 cm ISBN: 9781493901029 ; br. Note: This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations. Sujets MSC: 03C64 Mathematical logic and foundations -- Model theory -- Model theory of ordered structures; o-minimality
14P15 Algebraic geometry -- Real algebraic and real analytic geometry -- Real analytic and semianalytic sets
26Axx Real functions -- Functions of one variable
32C05 Several complex variables and analytic spaces -- Analytic spaces -- Real-analytic manifolds, real-analytic spaces
34C08 Ordinary differential equations -- Qualitative theory -- Connections with real algebraic geometry
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This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations.

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