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| Author | : David Marker |
| Publisher | : CRC Press |
| Total Pages | : 172 |
| Release | : 2005-12-15 |
| Genre | : Mathematics |
| ISBN | : 1439864411 |
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.
| Author | : David Marker |
| Publisher | : A K Peters/CRC Press |
| Total Pages | : 200 |
| Release | : 2005-12-15 |
| Genre | : Mathematics |
| ISBN | : 9781568812816 |
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.
| Author | : David Marker |
| Publisher | : Cambridge University Press |
| Total Pages | : 166 |
| Release | : 2017-03-02 |
| Genre | : Mathematics |
| ISBN | : 1316739325 |
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. 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 |
| Total Pages | : 210 |
| Release | : 2005-12-28 |
| Genre | : Mathematics |
| ISBN | : 354030035X |
Absolute 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 |
| Total Pages | : 342 |
| Release | : 2006-04-06 |
| Genre | : Mathematics |
| ISBN | : 0387227342 |
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 | : Jonathan Kirby |
| Publisher | : Cambridge University Press |
| Total Pages | : 197 |
| Release | : 2019-04-18 |
| Genre | : Mathematics |
| ISBN | : 1316732398 |
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.
| Author | : Neil Fligstein |
| Publisher | : Oxford University Press |
| Total Pages | : 253 |
| Release | : 2015 |
| Genre | : History |
| ISBN | : 0190241454 |
In 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 | : M Droste |
| Publisher | : CRC Press |
| Total Pages | : 516 |
| Release | : 1998-01-29 |
| Genre | : Mathematics |
| ISBN | : 9789056991012 |
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 | : Elisabeth Bouscaren |
| Publisher | : Springer |
| Total Pages | : 223 |
| Release | : 2009-03-14 |
| Genre | : Mathematics |
| ISBN | : 3540685219 |
This 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 | : Matthew D. Schwartz |
| Publisher | : Cambridge University Press |
| Total Pages | : 869 |
| Release | : 2014 |
| Genre | : Science |
| ISBN | : 1107034736 |
A modern introduction to quantum field theory for graduates, providing intuitive, physical explanations supported by real-world applications and homework problems.
