A Concise Introduction to Mathematical Logic

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Author: Wolfgang Rautenberg

Publisher: Springer Science & Business Media

ISBN: 0387342419

Category: Mathematics

Page: 256

View: 8295

While there are already several well known textbooks on mathematical logic this book is unique in treating the material in a concise and streamlined fashion. This allows many important topics to be covered in a one semester course. Although the book is intended for use as a graduate text the first three chapters can be understood by undergraduates interested in mathematical logic. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text.

Logic and Discrete Mathematics

A Concise Introduction, Solutions Manual

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Author: Willem Conradie,Valentin Goranko,Claudette Robinson

Publisher: John Wiley & Sons

ISBN: 1119000106

Category: Mathematics

Page: 200

View: 5544

Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in this accompanying solutions manual.

Lectures on Mathematical Logic

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Author: Walter Felscher

Publisher: CRC Press

ISBN: 9789056992675

Category: Mathematics

Page: 330

View: 3751

In this volume, logic starts from the observation that in everyday arguments, as brought forward by say a lawyer, statements are transformed linguistically, connecting them in formal ways irrespective of their contents. Understanding such arguments as deductive situations, or "sequents" in the technical terminology, the transformations between them can be expressed as logical rules. The book concludes with the algorithms producing the results of Gentzen's midsequent theorem and Herbrand's theorem for prenex formulas.

An Invitation to Morse Theory

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Author: Liviu Nicolaescu

Publisher: Springer Science & Business Media

ISBN: 038749510X

Category: Mathematics

Page: 242

View: 9879

This book offers readers a taste of the "unreasonable effectiveness" of Morse theory. It covers many of the most important topics in Morse theory along with applications. The book details topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. In addition, many examples, problems, and illustrations further enhance the value of this useful introduction to Morse Theory.

A Basic Course in Probability Theory

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Author: Rabi Bhattacharya,Edward C. Waymire

Publisher: Springer Science & Business Media

ISBN: 0387719385

Category: Mathematics

Page: 220

View: 1303

Introductory Probability is a pleasure to read and provides a fine answer to the question: How do you construct Brownian motion from scratch, given that you are a competent analyst? There are at least two ways to develop probability theory. The more familiar path is to treat it as its own discipline, and work from intuitive examples such as coin flips and conundrums such as the Monty Hall problem. An alternative is to first develop measure theory and analysis, and then add interpretation. Bhattacharya and Waymire take the second path.

Introduction to Model Theory

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Author: Philipp Rothmaler

Publisher: CRC Press

ISBN: 9789056992873

Category: Mathematics

Page: 324

View: 2223

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.

Model Theory : An Introduction

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Author: David Marker

Publisher: Springer Science & Business Media

ISBN: 9780387987606

Category: Mathematics

Page: 342

View: 3023

"Model theory is the branch of mathematical logic that examines what it means for a first-order sentence... to be true in a particular structure....This is a text for graduate students, mainly aimed at those specializing in logic, but also of interest for mathematicians outside logic who want to know what model theory can offer them...it is one which makes a good case for model theory as much more than a tool for specialist logicians." -- THE MATHEMATICAL GAZETTE

A Course on Mathematical Logic

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Author: Shashi Mohan Srivastava

Publisher: Springer Science & Business Media

ISBN: 1461457467

Category: Mathematics

Page: 198

View: 526

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.

Set Theoretical Logic-The Algebra of Models

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Author: W Felscher

Publisher: CRC Press

ISBN: 9789056992668

Category: Mathematics

Page: 296

View: 3011

This is an introduction to mathematical logic in which all the usual topics are presented: compactness and axiomatizability of semantical consequence, Löwenheim-Skolem-Tarski theorems, prenex and other normal forms, and characterizations of elementary classes with the help of ultraproducts. Logic is based exclusively on semantics: truth and satisfiability of formulas in structures are the basic notions. The methods are algebraic in the sense that notions such as homomorphisms and congruence relations are applied throughout in order to gain new insights. These concepts are developed and can be viewed as a first course on universal algebra. The approach to algorithms generating semantical consequences is algebraic as well: for equations in algebras, for propositional formulas, for open formulas of predicate logic, and for the formulas of quantifier logic. The structural description of logical consequence is a straightforward extension of that of equational consequence, as long as Boolean valued propositions and Boolean valued structures are considered; the reduction of the classical 2-valued case then depends on the Boolean prime ideal theorem.