Download Free Model Theory : An Introduction PDF by David Marker Full Book and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download Free Model Theory PDF by D. Marker Full Book and published by . This book was released on 2002 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introductory course in model theory emphasizing connections to algebra. It is an appropriate introduction both for graduate students interested in advanced work in model theory and for students and researchers in logic or algebra who want to learn the basic results and themes of model theory.
Download Free Introduction to Model Theory PDF by Philipp Rothmaler Full Book and published by CRC Press. This book was released on 2000-10-31 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download Free A Course in Model Theory PDF by Bruno Poizat Full Book and published by Springer Science & Business Media. This book was released on 2000-05-25 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download Free An Invitation to Model Theory PDF by Jonathan Kirby Full Book and published by Cambridge University Press. This book was released on 2019-04-18 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.
Download Free Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1 PDF by Raf Cluckers Full Book and published by Cambridge University Press. This book was released on 2011-09-22 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This first volume contains introductory texts on the model theory of valued fields, different approaches to non-Archimedean geometry, and motivic integration on algebraic varieties and non-Archimedean spaces.
Download Free A Course on Basic Model Theory PDF by Haimanti Sarbadhikari Full Book and published by Springer. This book was released on 2017-09-05 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book is an exposition of the fundamental ideas of model theory. It presents the necessary background from logic, set theory and other topics of mathematics. Only some degree of mathematical maturity and willingness to assimilate ideas from diverse areas are required. The book can be used for both teaching and self-study, ideally over two semesters. It is primarily aimed at graduate students in mathematical logic who want to specialise in model theory. However, the first two chapters constitute the first introduction to the subject and can be covered in one-semester course to senior undergraduate students in mathematical logic. The book is also suitable for researchers who wish to use model theory in their work.
Download Free Lectures on Infinitary Model Theory PDF by David Marker Full Book and published by Cambridge University Press. This book was released on 2016-10-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download Free Model Theory in Algebra, Analysis and Arithmetic PDF by Lou van den Dries Full Book and published by Springer. This book was released on 2014-09-20 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download Free Mathematical Logic and Model Theory PDF by Alexander Prestel Full Book and published by Springer. This book was released on 2011-08-27 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download Free A Guide to Classical and Modern Model Theory PDF by Annalisa Marcja Full Book and published by Springer Science & Business Media. This book was released on 2003 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. It is a lively and fertile research area which deserves the attention of the mathematical world. This volume-is easily accessible to young people and mathematicians unfamiliar with logic; -gives a terse historical picture of Model Theory; -introduces the latest developments in the area; -provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. A Guide to Classical and Modern Model Theory is for trainees and professional model theorists, mathematicians working in Algebra and Geometry and young people with a basic knowledge of logic.
Author :Olga Kharlampovich Publisher :Walter de Gruyter GmbH & Co KG Release Date :2021-05-10 ISBN :3110719711 Pages :244 pages Rating :4.0/5 (719 Download)
Download Free Groups and Model Theory PDF by Olga Kharlampovich Full Book and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-05-10 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an overview of developments in group theory motivated by model theory by key international researchers in the field. Topics covered include: stable groups and generalizations, model theory of nonabelian free groups and of rigid solvable groups, pseudofinite groups, approximate groups, topological dynamics, groups interpreting the arithmetic. The book is intended for mathematicians and graduate students in group theory and model theory. The book follows the course of the GAGTA (Geometric and Asymptotic Group Theory with Applications) conference series. The first book, "Complexity and Randomness in Group Theory. GAGTA book 1," can be found here: http://www.degruyter.com/books/978-3-11-066491-1 .
Download Free A Course in Model Theory PDF by Katrin Tent Full Book and published by Cambridge University Press. This book was released on 2012-03-08 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise introduction to current topics in model theory, including simple and stable theories.
Download Free Model Theory PDF by María Manzano Full Book and published by Oxford University Press. This book was released on 1999 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic languages are free from the ambiguities of natural languages, and are therefore specially suited for use in computing. Model theory is the branch of mathematical logic which concerns the relationship between mathematical structures and logic languages, and has become increasinglyimportant in areas such as computing, philosophy and linguistics. As the reasoning process takes place at a very abstract level, model theory applies to a wide variety of structures. It is also possible to define new structures and classify existing ones by establishing links between them. Theselinks can be very useful since they allow us to transfer our knowledge between related structures. This book provides a clear and readable introduction to the subject, and is suitable for both mathematicians and students from outside the subject. It includes some historically relevant informationbefore each major topic is introduced, making it a useful reference for non-experts. The motivation of the subject is constantly explained, and proofs are also explained in detail.
Download Free A Course in Model Theory PDF by Bruno Poizat Full Book and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download Free Philosophy and Model Theory PDF by Tim Button Full Book and published by Oxford University Press. This book was released on 2018 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theory is an important area of mathematical logic which has deep philosophical roots, many philosophical applications, and great philosophical interest in itself. The aim of this book is to introduce, organise, survey, and develop these connections between philosophy and model theory, for the benefit of philosophers and logicians alike.
Download Free Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 2 PDF by Raf Cluckers Full Book and published by Cambridge University Press. This book was released on 2011-09-22 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.
