Some Definability Questions In Structures Over The Reals And In General O Minimal Structures PDF Download
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Author | : Ya'acov Amos Peterzil |
Publisher | : |
Total Pages | : 190 |
Release | : 1991 |
Genre | : |
ISBN | : |
Download Some Definability Questions in Structures Over the Reals and in General O-minimal Structures Book in PDF, ePub and Kindle
Author | : Mário J. Edmundo |
Publisher | : Cuvillier Verlag |
Total Pages | : 223 |
Release | : 2005 |
Genre | : |
ISBN | : 386537557X |
Download O-minimal Structures Book in PDF, ePub and Kindle
Author | : |
Publisher | : World Scientific |
Total Pages | : 1191 |
Release | : |
Genre | : |
ISBN | : |
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Author | : Chris Miller |
Publisher | : Springer Science & Business Media |
Total Pages | : 247 |
Release | : 2012-09-14 |
Genre | : Mathematics |
ISBN | : 1461440416 |
Download Lecture Notes on O-Minimal Structures and Real Analytic Geometry Book in PDF, ePub and Kindle
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.
Author | : Athipat Thamrongthanyalak |
Publisher | : |
Total Pages | : 108 |
Release | : 2013 |
Genre | : |
ISBN | : |
Download Extensions and Smooth Approximations of Definable Functions in O-minimal Structures Book in PDF, ePub and Kindle
In 1934, H. Whitney presented a series of papers which discussed how to determine whether a function or a jet of order m is the restriction of a C^m function on R^n. In the first paper of the series, Whitney's Extension Theorem was proved. In the latter, Whitney answered special cases of the following question: Question. (Whitney's Extension Theorem, WEP_n, m) Let f be a continuous function from a closed subset of R^n. How can we determine whether f is the restriction of a C^m-function on R^n? In this dissertation, we work in o-minimal expansions of real closed ordered fields. Definable versions of Whitney's Extension Theorem and Whitney's Extension Problems will be discussed in this context. Definable set-valued maps are also studied; a definable version of Michael's Selection Theorem will be proved and used, in combination with a definable version of Whitney's Extension Theorem, to give a positive answer to a definable version of WEP_n,1. In addition to the above problems, we also discuss smoothing problems. This is inspired by a series of papers by A. Fischer. In this series, a construction of a definable C^m-approximation of a definable locally Lipschitz function is provided. Here, we also work in an o-minimal expansion of a real closed field and relax the condition further to just continuous.
Author | : Erich Grädel |
Publisher | : Springer Science & Business Media |
Total Pages | : 447 |
Release | : 2007-04-24 |
Genre | : Computers |
ISBN | : 3540004289 |
Download Finite Model Theory and Its Applications Book in PDF, ePub and Kindle
Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.
Author | : Lou Van den Dries |
Publisher | : Cambridge University Press |
Total Pages | : 196 |
Release | : 1998-05-07 |
Genre | : Mathematics |
ISBN | : 0521598389 |
Download Tame Topology and O-minimal Structures Book in PDF, ePub and Kindle
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.
Author | : Deirdre Haskell |
Publisher | : Cambridge University Press |
Total Pages | : 244 |
Release | : 2000-07-03 |
Genre | : Mathematics |
ISBN | : 9780521780681 |
Download Model Theory, Algebra, and Geometry Book in PDF, ePub and Kindle
Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Author | : Sy D. Friedman |
Publisher | : Walter de Gruyter |
Total Pages | : 240 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9783110167771 |
Download Fine Structure and Class Forcing Book in PDF, ePub and Kindle
No detailed description available for "Fine Structure and Class Forcing".
Author | : Viggo Stoltenberg-Hansen |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2017-03-30 |
Genre | : Mathematics |
ISBN | : 1108587143 |
Download Logic Colloquium '03 Book in PDF, ePub and Kindle
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-fourth publication in the Lecture Notes in Logic series, contains the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Helsinki, Finland, in August 2003. These articles include an extended tutorial on generalizing finite model theory, as well as seventeen original research articles spanning all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy.