Lectures in Model Theory
Author: Franziska Jahnke
Publisher:
Published: 2018
Total Pages:
ISBN-13: 9783037191842
DOWNLOAD EBOOK →Lanterna Rally
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Model Theory for Beginners. 15 Lectures
Author: Roman Kossak
Publisher:
Published: 2021-02-10
Total Pages: 152
ISBN-13: 9781848903616
DOWNLOAD EBOOK →This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability, classification of complete types, elementary extensions, categoricity, automorphisms, and saturation; all illustrated with examples that require neither advanced alegbra nor set theory. A full proof of the compactness theorem for countable languages and its applications are given, followed by a discussion of the Ehrefeucht-Mostowski technique for constructing models admitting automorphisms. Additional topics include recursive saturation, nonstandard models of arithmetic, Abraham Robinson's model-theoretic proof of Tarski's theorem on undefinability of truth, and the proof of the Infinite Ramsey Theorem using an elementary extension of the standard model of arithmetic.
Lectures in Model Theory
Author: Franziska Jahnke
Publisher:
Published: 2018
Total Pages:
ISBN-13: 9783037196847
DOWNLOAD EBOOK →Lectures on Algebraic Model Theory
Author: Bradd T. Hart
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 121
ISBN-13: 0821827057
DOWNLOAD EBOOK →This thin volume contains three sets of lecture notes, representing recent developments in differential scales, o-minimality, and tame convergence theory. The first lecture outlines the basics of differential fields, and then addresses topics like differential varieties and tangent bundles, Kolchin's logarithmic derivative, and Manin's construction. The second describes added exponentation, T-convexity and tame extensions, piecewise linearity, the Wilkie inequality, and the valuation property. And the third considers the structure and varieties of finite algebra. No index. c. Book News Inc.
An Invitation to Model Theory
Author: Jonathan Kirby
Publisher: Cambridge University Press
Published: 2019-04-18
Total Pages: 197
ISBN-13: 1316732398
DOWNLOAD EBOOK →Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
A Course in Model Theory
Author: Katrin Tent
Publisher: Cambridge University Press
Published: 2012-03-08
Total Pages: 259
ISBN-13: 052176324X
DOWNLOAD EBOOK →Concise introduction to current topics in model theory, including simple and stable theories.
Model Theory of Fields
Author: David Marker
Publisher: CRC Press
Published: 2005-12-15
Total Pages: 172
ISBN-13: 1439864411
DOWNLOAD EBOOK →The model theory of fields is a fascinating subject stretching from Tarski's work on the decidability of the theories of the real and complex fields to Hrushovksi's recent proof of the Mordell-Lang conjecture for function fields. This volume provides an insightful introduction to this active area, concentrating on connections to stability theory.
Model Theory for Beginners. 15 Lectures
Author: Roman Kossak
Publisher:
Published: 2021-02-10
Total Pages: 152
ISBN-13: 9781848903616
DOWNLOAD EBOOK →This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability, classification of complete types, elementary extensions, categoricity, automorphisms, and saturation; all illustrated with examples that require neither advanced alegbra nor set theory. A full proof of the compactness theorem for countable languages and its applications are given, followed by a discussion of the Ehrefeucht-Mostowski technique for constructing models admitting automorphisms. Additional topics include recursive saturation, nonstandard models of arithmetic, Abraham Robinson's model-theoretic proof of Tarski's theorem on undefinability of truth, and the proof of the Infinite Ramsey Theorem using an elementary extension of the standard model of arithmetic.
Model Theory and Topoi
Author: F.W. Lawvere
Publisher: Springer
Published: 2006-11-15
Total Pages: 352
ISBN-13: 3540374957
DOWNLOAD EBOOK →A Collection of Lectures by Variuos Authors
Lectures on Stochastic Programming
Author: Alexander Shapiro
Publisher: SIAM
Published: 2009-01-01
Total Pages: 447
ISBN-13: 0898718759
DOWNLOAD EBOOK →Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.
