About this product

Product Identifiers

PublisherOxford University Press, Incorporated

ISBN-100198500505

ISBN-139780198500506

eBay Product ID (ePID)1790348

Product Key Features

Number of Pages352 Pages

Publication NameMathematical Logic Pt. 2 : A Course with ExercisesPart II: Recursion Theory, Gödel's Theorems, Set Theory, Model Theory

LanguageEnglish

Publication Year2001

SubjectLogic

TypeTextbook

Subject AreaMathematics

AuthorDaniel Lascar, Donald Pelletier, René Cori

FormatUk-Trade Paper

Dimensions

Item Height0.7 in

Item Weight17.7 Oz

Item Length9.2 in

Item Width6.1 in

Additional Product Features

Intended AudienceCollege Audience

Reviews"An undergraduate course text for students who have acquired the practice and knowledge of classical mathematics as taught in high school and the first year of college, but no specialized knowledge. Introducing the logic underlying mathematics and theoretical computer science, Cori and Lascar (both U. Paris VII) use the concept of model as their underlying theme. Pelletier (York U. Toronto) has clarified some of the terminology in English for beginning students."--SciTech Book News "I have always been especially fond of logic. The two-volumeMathematical Logic: A Course with Exercisesis a comprehensive introductory course that is distinguished by clarity of exposition and a large number of exercises with thorough solutions. Each volume is about 330 pages long, 80 of which are solutions!"The Bulletin of Mathematics Books, "An undergraduate course text for students who have acquired the practice and knowledge of classical mathematics as taught in high school and the first year of college, but no specialized knowledge. Introducing the logic underlying mathematics and theoretical computer science, Cori and Lascar (both U. Paris VII) use the concept of model as their underlying theme. Pelletier (York U. Toronto) has clarified some of the terminology in English for beginning students."--SciTech Book News"I have always been especially fond of logic. The two-volume Mathematical Logic: A Course with Exercises is a comprehensive introductory course that is distinguished by clarity of exposition and a large number of exercises with thorough solutions. Each volume is about 330 pages long, 80 of which are solutions!"The Bulletin of Mathematics Books, "An undergraduate course text for students who have acquired the practice and knowledge of classical mathematics as taught in high school and the first year of college, but no specialized knowledge. Introducing the logic underlying mathematics and theoretical computer science, Cori and Lascar (both U. Paris VII) use the concept of model as their underlying theme. Pelletier (York U. Toronto) has clarified some of the terminology in English for beginning students."--SciTech Book News "I have always been especially fond of logic. The two-volume Mathematical Logic: A Course with Exercises is a comprehensive introductory course that is distinguished by clarity of exposition and a large number of exercises with thorough solutions. Each volume is about 330 pages long, 80 of which are solutions!"The Bulletin of Mathematics Books

Dewey Edition21

Dewey Decimal511.3

Table Of ContentContents of Part INotes from the translatorNotes to the readerIntroduction5. Recursion theory5.1. Primitive recursive functions and sets5.2. Recursive functions5.3. Turing machines5.4. Recursively enumerable sets5.5. Exercises for Chapter 56. Formalization of arithmetic, Gödel's theorems6.1. Peano's axioms6.2. Representable functions6.3. Arithmetization of syntax6.4. Incompleteness and undecidability theorem7. Set theory7.1. The theories Z and ZF7.2. Ordinal numbers and integers7.3. Inductive proofs and definitions7.4. Cardinality7.5. The axiom of foundation and the reflections schemes7.6. Exercises for Chapter 78. Some model theory8.1. Elementary substructures and extensions8.2. Construction of elementary extensions8.3. The interpolation and definability theorems8.4. Reduced products and ultraproducts8.5. Preservations theorems8.6. -categorical theories8.7. Exercises for Chapter 8Solutions to the exercises of Part IIChapter 5Chapter 6Chapter 7Chapter 8BibliographyIndex

SynopsisLogic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. It is a major element in theoretical computer science and has undergone a huge revival with the every- growing importance of computer science. This text is based on a course to undergraduates and provides a clear and accessible introduction to mathematical logic. The concept of model provides the underlying theme, giving the text a theoretical coherence whilst still covering a wide area of logic. The foundations having been laid in Part I, this book starts with recursion theory, a topic essential for the complete scientist. Then follows Godel's incompleteness theorems and axiomatic set theory. Chapter 8 provides an introduction to model theory. There are examples throughout each section, and varied selection of exercises at the end. Answers to the exercises are given in the appendix., The requirement to reason logically forms the basis of all mathematics, and hence mathematical logic is one of the most fundamental topics that students will study. Assuming no prior knowledge of the topic, this book provides an accessible introduction for advanced undergraduate students., Logic forms the basis of mathematics, and is hence a fundamental part of any mathematics course. It is a major element in theoretical computer science and has undergone a huge revival with the ever-growing importance of computer science. This text is based on a course to undergraduates and provides a clear and accessible introduction to mathematical logic. The concept of model provides the underlying theme, giving the text a theoretical coherence whilst still covering a wide area of logic. The foundations having been laid in Part 1, this book starts with recursion theory, a topic essential for the complete scientist. Then follows Godel's incompleteness theorems and axiomatic set theory. Chapter 8 provides an introduction to model theory. There are examples throughout each section, and varied selection of exercises at the end. Answers to the exercises are given in the appendix.