Download mathematical logic and model theory a brief introduction universitext in pdf or read mathematical logic and model theory a brief introduction universitext in pdf online books in PDF, EPUB and Mobi Format. Click Download or Read Online button to get mathematical logic and model theory a brief introduction universitext in pdf book now. This site is like a library, Use search box in the widget to get ebook that you want.



Mathematical Logic And Model Theory

Author: Alexander Prestel
Publisher: Springer Science & Business Media
ISBN: 1447121767
Size: 43.59 MB
Format: PDF, ePub
View: 5341
Download and Read
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.

A Course In Model Theory

Author: Bruno Poizat
Publisher: Springer Science & Business Media
ISBN: 1441986227
Size: 71.65 MB
Format: PDF, Kindle
View: 6508
Download and Read
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.

A Course On Mathematical Logic

Author: Shashi Mohan Srivastava
Publisher: Springer Science & Business Media
ISBN: 1461457467
Size: 78.20 MB
Format: PDF
View: 2936
Download and Read
This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.

A Concise Introduction To Mathematical Logic

Author: Wolfgang Rautenberg
Publisher: Springer
ISBN: 9781441912213
Size: 62.76 MB
Format: PDF
View: 6825
Download and Read
Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

Logic And Structure

Author: Dirk van Dalen
Publisher: Springer Science & Business Media
ISBN: 3662029626
Size: 54.44 MB
Format: PDF, Kindle
View: 2832
Download and Read
New corrected printing of a well-established text on logic at the introductory level.

Fundamentals Of Mathematical Logic

Author: Peter G. Hinman
Publisher: CRC Press
ISBN: 1439864276
Size: 20.39 MB
Format: PDF, ePub
View: 3519
Download and Read
This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

Logical Number Theory I

Author: Craig Smorynski
Publisher: Springer Science & Business Media
ISBN: 3642754627
Size: 43.51 MB
Format: PDF, ePub
View: 6702
Download and Read
Number theory as studied by the logician is the subject matter of the book. This first volume can stand on its own as a somewhat unorthodox introduction to mathematical logic for undergraduates, dealing with the usual introductory material: recursion theory, first-order logic, completeness, incompleteness, and undecidability. In addition, its second chapter contains the most complete logical discussion of Diophantine Decision Problems available anywhere, taking the reader right up to the frontiers of research (yet remaining accessible to the undergraduate). The first and third chapters also offer greater depth and breadth in logico-arithmetical matters than can be found in existing logic texts. Each chapter contains numerous exercises, historical and other comments aimed at developing the student's perspective on the subject, and a partially annotated bibliography.

An Introduction To Mathematical Logic And Type Theory

Author: Peter B. Andrews
Publisher: Springer Science & Business Media
ISBN: 9401599343
Size: 60.56 MB
Format: PDF, ePub, Mobi
View: 844
Download and Read
In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.

Toposes And Local Set Theories

Author: John L. Bell
Publisher: Courier Corporation
ISBN: 0486462862
Size: 24.62 MB
Format: PDF, ePub, Mobi
View: 7443
Download and Read
This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.

Categorical Logic And Type Theory

Author: Bart Jacobs
Publisher: Gulf Professional Publishing
ISBN: 9780444508539
Size: 16.14 MB
Format: PDF, Kindle
View: 2144
Download and Read
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.