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Author: Lou Van den Dries
Publisher: Cambridge University Press
Published: 1998-05-07
Total Pages: 196
ISBN-13: 0521598389
DOWNLOAD EBOOKThese 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: Lou Van den Dries
Publisher:
Published: 1998
Total Pages: 180
ISBN-13: 9781107365063
DOWNLOAD EBOOKThese notes give a self-contained treatment of the theory of o-minimal structures.
Author: Mário J. Edmundo
Publisher: Cuvillier Verlag
Published: 2005
Total Pages: 223
ISBN-13: 386537557X
DOWNLOAD EBOOKAuthor: G. O. Jones
Publisher: Cambridge University Press
Published: 2015-08-13
Total Pages: 235
ISBN-13: 1107462495
DOWNLOAD EBOOKThis book brings the researcher up to date with recent applications of mathematical logic to number theory.
Author: Chris Miller
Publisher: Springer Science & Business Media
Published: 2012-09-14
Total Pages: 247
ISBN-13: 1461440424
DOWNLOAD EBOOKThis 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: Deirdre Haskell
Publisher: Cambridge University Press
Published: 2000-07-03
Total Pages: 244
ISBN-13: 9780521780681
DOWNLOAD EBOOKModel theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications range from a proof of the rationality of certain Poincare series associated to varieties over p-adic fields, to a proof of the Mordell-Lang conjecture for function fields in positive characteristic. In some cases (such as the latter) it is the most abstract aspects of model theory which are relevant. This book, originally published in 2000, arising from a series of introductory lectures for graduate students, provides the necessary background to understanding both the model theory and the mathematics behind these applications. The book is unique in that the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations) is covered and diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) are introduced and discussed, all by leading experts in their fields.
Author: Pierre Simon
Publisher: Cambridge University Press
Published: 2015-07-16
Total Pages: 165
ISBN-13: 1107057752
DOWNLOAD EBOOKThe first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.
Author: Jonathan Pila
Publisher: Cambridge University Press
Published: 2022-06-09
Total Pages: 268
ISBN-13: 1009301926
DOWNLOAD EBOOKPoint-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.
Author: David Marker
Publisher: Springer Science & Business Media
Published: 2006-04-06
Total Pages: 342
ISBN-13: 0387227342
DOWNLOAD EBOOKAssumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures
Author: S. S. Goncharov
Publisher: World Scientific
Published: 2006
Total Pages: 329
ISBN-13: 981277274X
DOWNLOAD EBOOKThis volume is devoted to the main areas of mathematical logic and applications to computer science. There are articles on weakly o-minimal theories, algorithmic complexity of relations, models within the computable model theory, hierarchies of randomness tests, computable numberings, and complexity problems of minimal unsatisfiable formulas. The problems of characterization of the deduction-detachment theorem, o 1 -induction, completeness of Leoniewski''s systems, and reduction calculus for the satisfiability problem are also discussed. The coverage includes the answer to Kanovei''s question about the upper bound for the complexity of equivalence relations by convergence at infinity for continuous functions. The volume also gives some applications to computer science such as solving the problems of inductive interference of languages from the full collection of positive examples and some negative data, the effects of random negative data, methods of formal specification and verification on the basis of model theory and multiple-valued logics, interval fuzzy algebraic systems, the problems of information exchange among agents on the base topological structures, and the predictions provided by inductive theories. Sample Chapter(s). Chapter 1: Another Characterization of the Deduction-Detachment Theorem (535 KB). Contents: Another Characterization of the Deduction-Detachment Theorem (S V Babyonyshev); On Behavior of 2-Formulas in Weakly o-Minimal Theories (B S Baizhanov & B Sh Kulpeshov); Arithmetic Turing Degrees and Categorical Theories of Computable Models (E Fokina); Negative Data in Learning Languages (S Jain & E Kinber); Effective Cardinals in the Nonstandard Universe (V Kanovei & M Reeken); Model-Theoretic Methods of Analysis of Computer Arithmetic (S P Kovalyov); The Functional Completeness of Leoniewski''s Systems (F Lepage); Hierarchies of Randomness Tests (J Reimann & F Stephan); Intransitive Linear Temporal Logic Based on Integer Numbers, Decidability, Admissible Logical Consecutions (V V Rybakov); The Logic of Prediction (E Vityaev); Conceptual Semantic Systems Theory and Applications (K E Wolff); Complexity Results on Minimal Unsatisfiable Formulas (X Zhao); and other papers. Readership: Researchers in mathematical logic and algebra, computer scientists in artificial intelligence and fuzzy logic."
