## Tame Topology and O-minimal Structures

Author: L. P. D. van den Dries
Publisher: Cambridge University Press
ISBN: 0521598389
Category : Mathematics
Languages : en
Pages : 196
Book Description
These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.

## O-minimal Structures

Author: Mário J. Edmundo
Publisher: Cuvillier Verlag
ISBN: 386537557X
Category :
Languages : en
Pages : 223
Book Description

## Lecture Notes on O-Minimal Structures and Real Analytic Geometry

Author: Chris Miller
Publisher: Springer Science & Business Media
ISBN: 1461440416
Category : Mathematics
Languages : en
Pages : 247
Book Description
​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. ​

## Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)

Author: Ehud Hrushovski
Publisher: Princeton University Press
ISBN: 1400881226
Category : Mathematics
Languages : en
Pages : 232
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.

## Logic Colloquium 2005

Author: Costas Dimitracopoulos
Publisher: Cambridge University Press
ISBN: 1139467255
Category : Mathematics
Languages : en
Pages : 272
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.

## Tame Flows

Author: Liviu I. Nicolaescu
Publisher: American Mathematical Soc.
ISBN: 0821848704
Category : Mathematics
Languages : en
Pages : 130
Book Description
The tame flows are nice'' flows on nice'' spaces. The nice (tame) sets are the pfaffian sets introduced by Khovanski, and a flow $\Phi: \mathbb{R}\times X\rightarrow X$ on pfaffian set $X$ is tame if the graph of $\Phi$ is a pfaffian subset of $\mathbb{R}\times X\times X$. Any compact tame set admits plenty tame flows. The author proves that the flow determined by the gradient of a generic real analytic function with respect to a generic real analytic metric is tame.

## Logic Colloquium 2007

Author: Françoise Delon
Publisher: Cambridge University Press
ISBN: 1139488937
Category : Mathematics
Languages : en
Pages : 267
Book Description
The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay's conjecture, and on automatic structures. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.

## Computational Aspects of General Equilibrium Theory

Author: Donald Brown
Publisher: Springer Science & Business Media
ISBN: 3540765913
Category : Business & Economics
Languages : en
Pages : 204
Book Description
This monograph presents a general equilibrium methodology for microeconomic policy analysis. It is intended to serve as an alternative to the now classical, axiomatic general equilibrium theory as exposited in Debreus Theory of Value (1959) or Arrow and Hahns General Competitive Analysis (1971). The monograph consists of several essays written over the last decade. It also contains an appendix by Charles Steinhorn on the elements of O-minimal structures.

## Hybrid Systems: Computation and Control

Author: Frits W. Vaandrager
Publisher: Springer
ISBN: 3540489835
Category : Computers
Languages : en
Pages : 282
Book Description
This volume contains the proceedings of the Second International Workshop on Hybrid Systems: Computation and Control (HSCC’99) to be held March 29- 31, 1999, in the village Berg en Dal near Nijmegen, The Netherlands. The rst workshop of this series was held in April 1998 at the University of California at Berkeley. The series follows meetings that were initiated by Anil Nerode at Cornell University. The proceedings of those meetings were published in the Springer-Verlag LNCS Series, Volumes 736, 999, 1066, 1201, and 1273. The p- ceedings of the rst workshop of the new series was published in LNCS 1386. The focus of the workshop is on modeling, control, synthesis, design, and ve- cation of hybrid systems. A hybrid system is a theoretical model for a computer controlled engineering system, with a dynamics that evolves both in a discrete state set and in a family of continuous state spaces. Research is motivated by, for example, control of electro-mechanical systems (robots), air tra c control, control of automated freeways, and chemical process control. The emerging - search area of hybrid systems overlaps both with computer science and with control theory. The interaction between researchers from these elds is expected to be fruitfull for the development of the area of hybrid systems.

## Topology of Singular Spaces and Constructible Sheaves

Author: Jörg Schürmann
Publisher: Birkhäuser
ISBN: 3034880618
Category : Mathematics
Languages : en
Pages : 454
Book Description
This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.