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Author: David Marker
Publisher: CRC Press
Published: 2005-12-15
Total Pages: 172
ISBN-13: 1439864411
DOWNLOAD EBOOKThe 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.
Author: David Marker
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 166
ISBN-13: 1316739325
DOWNLOAD EBOOKSince 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. In this volume, the fifth publication in the Lecture Notes in Logic series, the authors give an insightful introduction to the fascinating subject of the model theory of fields, concentrating on its connections to stability theory. In the first two chapters David Marker gives an overview of the model theory of algebraically closed, real closed and differential fields. In the third chapter Anand Pillay gives a proof that there are 2א non-isomorphic countable differential closed fields. Finally, Margit Messmer gives a survey of the model theory of separably closed fields of characteristic p > 0.
Author: Antonio J. Engler
Publisher: Springer Science & Business Media
Published: 2005-12-28
Total Pages: 210
ISBN-13: 354030035X
DOWNLOAD EBOOKAbsolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.
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: Neil Fligstein
Publisher: Oxford University Press
Published: 2015
Total Pages: 253
ISBN-13: 0190241454
DOWNLOAD EBOOKIn recent years there has been an outpouring of work at the intersection of social movement thoery, organizational theory, economic, and political sociology. The problems at the core of these areas, Fligstein and McAdam argue, have a similar analytic and theoretical structure. Synthesizing much of this work, A Theory of Fields offers a general perspective on how to understand the problems related to understanding change and instability in modern, complex societies through a theory of strategic action fields.
Author: Elisabeth Bouscaren
Publisher: Springer
Published: 2009-03-14
Total Pages: 223
ISBN-13: 3540685219
DOWNLOAD EBOOKThis introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Author: Jonathan Kirby
Publisher: Cambridge University Press
Published: 2019-04-18
Total Pages: 197
ISBN-13: 1316732398
DOWNLOAD EBOOKModel 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.
Author: Deirdre Haskell
Publisher: Cambridge University Press
Published: 2000-07-03
Total Pages: 244
ISBN-13: 9780521780681
DOWNLOAD EBOOKLeading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Author: Matthias Aschenbrenner
Publisher: Princeton University Press
Published: 2017-06-06
Total Pages: 873
ISBN-13: 0691175438
DOWNLOAD EBOOKAsymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
Author: C.C. Chang
Publisher: Courier Corporation
Published: 2013-10-03
Total Pages: 674
ISBN-13: 0486310957
DOWNLOAD EBOOKThis bestselling textbook for higher-level courses was extensively revised in 1990 to accommodate developments in model theoretic methods. Topics include models constructed from constants, ultraproducts, and saturated and special models. 1990 edition.
