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Author: Bradd T. Hart
Publisher: American Mathematical Soc.
ISBN: 0821827057
Category : Mathematics
Languages : en
Pages : 121
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Book Description
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.
Author: Bradd T. Hart
Publisher: American Mathematical Soc.
ISBN: 0821827057
Category : Mathematics
Languages : en
Pages : 121
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Book Description
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.
Author: Bradd T. Hart
Publisher: Springer Science & Business Media
ISBN: 9401589232
Category : Mathematics
Languages : en
Pages : 285
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Book Description
Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.
Author: Shreeram Shankar Abhyankar
Publisher: World Scientific
ISBN: 9812568263
Category : Mathematics
Languages : en
Pages : 758
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Book Description
This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.
Author: Lou van den Dries
Publisher: Springer
ISBN: 3642549365
Category : Mathematics
Languages : en
Pages : 201
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Book Description
Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Author: David Marker
Publisher: Cambridge University Press
ISBN: 1316858081
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory.
Author: M Droste
Publisher: CRC Press
ISBN: 1000725278
Category : Mathematics
Languages : en
Pages : 516
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Book Description
Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.
Author: Deirdre Haskell
Publisher: Cambridge University Press
ISBN: 9780521780681
Category : Mathematics
Languages : en
Pages : 244
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Book Description
Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Author: P. Mangani
Publisher: Springer Science & Business Media
ISBN: 3642111211
Category : Mathematics
Languages : en
Pages : 151
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Book Description
Lectures: G.E. Sacks: Model theory and applications.- H.J. Keisler: Constructions in model theory.- Seminars: M. Servi: SH formulas and generalized exponential.- J.A. Makowski: Topological model theory.
Author: David Marker
Publisher: Springer Science & Business Media
ISBN: 0387227342
Category : Mathematics
Languages : en
Pages : 342
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Book Description
Assumes 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: Franziska Jahnke
Publisher:
ISBN: 9783037196847
Category :
Languages : en
Pages :
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Book Description
