Model Theory : An Introduction - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Model Theory : An Introduction write by David Marker. This book was released on 2006-04-06. Model Theory : An Introduction available in PDF, EPUB and Kindle. 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
Introduction to Model Theory
Introduction to Model Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Model Theory write by Philipp Rothmaler. This book was released on 2018-12-07. Introduction to Model Theory available in PDF, EPUB and Kindle. Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
A Course in Model Theory
A Course in Model Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course in Model Theory write by Bruno Poizat. This book was released on 2012-12-06. A Course in Model Theory available in PDF, EPUB and Kindle. Translated from the French, this book is an introduction to first-order model theory. Starting from scratch, it quickly reaches the essentials, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.
An Invitation to Model Theory
An Invitation to Model Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to Model Theory write by Jonathan Kirby. This book was released on 2019-04-18. An Invitation to Model Theory available in PDF, EPUB and Kindle. 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.
Mathematical Logic and Model Theory
Mathematical Logic and Model Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematical Logic and Model Theory write by Alexander Prestel. This book was released on 2011-08-21. Mathematical Logic and Model Theory available in PDF, EPUB and Kindle. 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.
