Model Theory In Algebra Analysis And Arithmetic

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Model Theory In Algebra Analysis And Arithmetic

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Author : Lou van den Dries
language : en
Publisher: Springer
Release Date : 2014-09-20

Model Theory In Algebra Analysis And Arithmetic written by Lou van den Dries and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-20 with Mathematics categories.

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.

Mathematical Logic And Model Theory

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Author : Alexander Prestel
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-21

Mathematical Logic And Model Theory written by Alexander Prestel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-21 with Mathematics categories.

Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.

Model Theory Algebra And Geometry

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Author : Deirdre Haskell
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-03

Model Theory Algebra And Geometry written by Deirdre Haskell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-03 with Mathematics categories.

Model 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.

Nonstandard Models Of Arithmetic And Set Theory

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Author : Ali Enayat
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Nonstandard Models Of Arithmetic And Set Theory written by Ali Enayat and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD). The volume opens with an essay from Haim Gaifman that probes the concept of non-standardness in mathematics and provides a fascinating mix of historical and philosophical insights into the nature of nonstandard mathematical structures. In particular, Gaifman compares and contrasts the discovery of nonstandard models with other key mathematical innovations, such as the introduction of various number systems, the modern concept of function, and non-Euclidean geometries. Other articles in the book present results related to nonstandard models in arithmetic and set theory, including a survey of known results on the Turing upper bounds of arithmetic sets and functions. The volume is suitable for graduate students and research mathematicians interested in logic, especially model theory.

Model Theory And Algebra

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Author : D.H. Saracino
language : en
Publisher: Springer
Release Date : 2006-11-14

Model Theory And Algebra written by D.H. Saracino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Philosophy And Model Theory

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Author : Tim Button
language : en
Publisher: Oxford University Press
Release Date : 2018-03-09

Philosophy And Model Theory written by Tim Button and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-09 with Philosophy categories.

Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.

Representation Theory And Algebraic Geometry

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Author : A. Martsinkovsky
language : en
Publisher: Cambridge University Press
Release Date : 1997-05-15

Representation Theory And Algebraic Geometry written by A. Martsinkovsky and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-15 with Mathematics categories.

For any researcher working in representation theory, algebraic or arithmetic geometry.

Model Theory

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Author : C.C. Chang
language : en
Publisher: Courier Corporation
Release Date : 2013-10-03

Model Theory written by C.C. Chang and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-03 with Mathematics categories.

This 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.

Algebraic Models In Geometry

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Author : Yves Félix
language : en
Publisher: OUP Oxford
Release Date : 2008-03-13

Algebraic Models In Geometry written by Yves Félix and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-13 with Mathematics categories.

Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also for geometers who are faced with problems requiring topological approaches and thus need a simple and concrete introduction to rational homotopy. This is essentially a book of applications. Geodesics, curvature, embeddings of manifolds, blow-ups, complex and Kähler manifolds, symplectic geometry, torus actions, configurations and arrangements are all covered. The chapters related to these subjects act as an introduction to the topic, a survey, and a guide to the literature. But no matter what the particular subject is, the central theme of the book persists; namely, there is a beautiful connection between geometry and rational homotopy which both serves to solve geometric problems and spur the development of topological methods.

Model Theory An Introduction

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Author : David Marker
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06

Model Theory An Introduction written by David Marker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.

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