Mathematical Logic And Model Theory

Author : Alexander Prestel,Charles N. Delzell
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 53,9 Mb
Release : 2011-08-21
Category : Mathematics
ISBN : 9781447121763

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Mathematical Logic and Model Theory by Alexander Prestel,Charles N. Delzell Pdf

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.

Author : Bruno Poizat
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781441986221

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A Course in Model Theory by Bruno Poizat Pdf

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.

Author : Heinz-Dieter Ebbinghaus
Publisher : Springer Science & Business Media
Page : 653 pages
File Size : 55,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662090589

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Ω-Bibliography of Mathematical Logic by Heinz-Dieter Ebbinghaus Pdf

Gert H. Müller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg 11. Non-classical Logics W. Rautenberg 111. Model Theory H.-D. Ebbinghaus IV. Recursion Theory P.G. Hinman V. Set Theory A.R. Blass VI. ProofTheory; Constructive Mathematics J.E. Kister; D. van Dalen & A.S. Troelstra.

Author : Alexander Prestel,Charles Delzell
Publisher : Springer
Page : 194 pages
File Size : 43,8 Mb
Release : 2011-08-27
Category : Mathematics
ISBN : 1447121775

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Mathematical Logic and Model Theory by Alexander Prestel,Charles Delzell Pdf

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.

Author : Jerome Malitz
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461394419

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Introduction to Mathematical Logic by Jerome Malitz Pdf

This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III. An attempt has been made to develop the beginning of each part slowly and then to gradually quicken the pace and the complexity of the material. Each part ends with a brief introduction to selected topics of current interest. The text is divided into three parts: one dealing with set theory, another with computable function theory, and the last with model theory. Part III relies heavily on the notation, concepts and results discussed in Part I and to some extent on Part II. Parts I and II are independent of each other, and each provides enough material for a one semester course. The exercises cover a wide range of difficulty with an emphasis on more routine problems in the earlier sections of each part in order to familiarize the reader with the new notions and methods. The more difficult exercises are accompanied by hints. In some cases significant theorems are devel oped step by step with hints in the problems. Such theorems are not used later in the sequence.

Author : Georg Kreisel,Jean Louis Krivine
Publisher : Elsevier
Page : 222 pages
File Size : 45,5 Mb
Release : 1967
Category : Electronic books
ISBN : 0444534121

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Elements of Mathematical Logic by Georg Kreisel,Jean Louis Krivine Pdf

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 48,5 Mb
Release : 1973
Category : Model theory
ISBN : 0720422000

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Model Theory by Anonim Pdf

Author : David Marker
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 55,8 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227344

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Model Theory : An Introduction by David Marker Pdf

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 : Georg Kreisel,Jean Louis Krivine
Publisher : Unknown
Page : 244 pages
File Size : 47,5 Mb
Release : 1967
Category : Logic, Symbolic and mathematical
ISBN : UOM:39015070586394

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Elements of Mathematical Logic by Georg Kreisel,Jean Louis Krivine Pdf

This book presents the principles of the Axiomatic Method, here formulated in set theoretic, also called: semantic, terms. This book also contains the elementary, more or less classical, results of its subject. Each of its eight chapters is preceded by a summary which not only indicates the general content of the chapter, but also the relation of the exercises to the main theorems.

Author : Haimanti Sarbadhikari,Shashi Mohan Srivastava
Publisher : Springer
Page : 291 pages
File Size : 47,5 Mb
Release : 2017-09-05
Category : Mathematics
ISBN : 9789811050985

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A Course on Basic Model Theory by Haimanti Sarbadhikari,Shashi Mohan Srivastava Pdf

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.

Author : Jonathan Kirby
Publisher : Cambridge University Press
Page : 197 pages
File Size : 49,5 Mb
Release : 2019-04-18
Category : Mathematics
ISBN : 9781107163881

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An Invitation to Model Theory by Jonathan Kirby Pdf

An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.

Author : H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 49,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475723557

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Mathematical Logic by H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas Pdf

This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Author : John T. Baldwin
Publisher : Cambridge University Press
Page : 365 pages
File Size : 43,6 Mb
Release : 2018-01-25
Category : Mathematics
ISBN : 9781107189218

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Model Theory and the Philosophy of Mathematical Practice by John T. Baldwin Pdf

Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.

Author : Jose Iovino
Publisher : CRC Press
Page : 327 pages
File Size : 41,7 Mb
Release : 2023-07-03
Category : Mathematics
ISBN : 9780429554193

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Beyond First Order Model Theory, Volume II by Jose Iovino Pdf

A coherent introduction to current trends in model theory Contains articles by some of the most influential logicians of the last hundred years. No other publication brings these distinguished authors together Suitable as a reference for advanced undergraduate, postgraduates, and researchers Material presented in the book (e.g, abstract elementary classes, first-order logics with dependent sorts, and applications of infinitary logics in set theory) is not easily accessible in the current literature The various chapters in the book can be studied independently.

Author : Heinz-Dieter Ebbinghaus,Jörg Flum
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 50,8 Mb
Release : 2005-12-29
Category : Mathematics
ISBN : 9783540287889

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Finite Model Theory by Heinz-Dieter Ebbinghaus,Jörg Flum Pdf

This is a thoroughly revised and enlarged second edition that presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently.