Mathematical Logic: Part 2: Recursion Theory, Godel's Theorems, Set Theory, Mode

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Mathematical Logic: Part 2 by Daniel Lascar, Donald Pelletier, René Cori

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.

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

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 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 stillcovering 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 incompletenesstheorems 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.

Table of Contents

Introduction 5: Recursion theory 5.1: Primitive recursive functions and sets 5.2: Recursive functions 5.3: Turing machines 5.4: Recursively enumerable sets 5.5: Exercises for Chapter 5 6: Formalization of arithmetic, Godel's theorems 6.1: Peano's axioms 6.2: Representable functions 6.3: Arithmetization of syntax 6.4: Incompleteness and undecidability theorem 7: Set theory 7.1: The theories Z and ZF 7.2: Ordinal numbers and integers 7.3: Inductive proofs and definitions 7.4: Cardinality 7.5: The axiom of foundation and the reflections schemes 7.6: Exercises for Chapter 7 8: Some model theory 8.1: Elementary substructures and extensions 8.2: Construction of elementary extensions 8.3: The interpolation and definability theorems 8.4: Reduced products and ultraproducts 8.5: Preservations theorems 8.6: -categorical theories 8.7: Exercises for Chapter 8 Solutions to the exercises of Part II Chapter 5 Chapter 6 Chapter 7 Chapter 8 Bibliography Index

Review

"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

Long Description

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 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 stillcovering 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 areexamples throughout each section, and varied selection of exercises at the end. Answers to the exercises are given in the appendix.

Review Text

Introduction 5. Recursion theory 5.1. Primitive recursive functions and sets 5.2. Recursive functions 5.3. Turing machines 5.4. Recursively enumerable sets 5.5. Exercises for Chapter 5 6. Formalization of arithmetic, Godel's theorems 6.1. Peano's axioms 6.2. Representable functions 6.3. Arithmetization of syntax 6.4. Incompleteness and undecidability theorem 7. Set theory 7.1. The theories Z and ZF 7.2. Ordinal numbers and integers 7.3. Inductive proofs and definitions 7.4. Cardinality 7.5. The axiom of foundation and the reflections schemes 7.6. Exercises for Chapter 7 8. Some model theory 8.1. Elementary substructures and extensions 8.2. Construction of elementary extensions 8.3. The interpolation and definability theorems 8.4. Reduced products and ultraproducts 8.5. Preservations theorems 8.6. -categorical theories 8.7. Exercises for Chapter 8 Solutions to the exercises of Part II Chapter 5 Chapter 6 Chapter 7 Chapter 8 Bibliography Index

Review Quote

"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

Feature

Based on a successful courseClear exposition, translation of successful textAuthors are internationally respectedGap in the market for text that covers a complete course in mathematical logic

Details ISBN0198500513 Author René Cori Short Title MATHEMATICAL LOGIC Pages 352 Language English ISBN-10 0198500513 ISBN-13 9780198500513 Media Book Format Hardcover DEWEY 511.3 Year 2001 Translator Donald Pelletier Imprint Oxford University Press Place of Publication Oxford Country of Publication United Kingdom Translated from French Illustrations black & white illustrations Series Mathematical Logic Subtitle Recursion Theory, Godel's Theorems, Set Theory, Model Theory DOI 10.1604/9780198500513 UK Release Date 2001-04-12 NZ Release Date 2001-04-12 Publisher Oxford University Press Publication Date 2001-04-12 Alternative 9780198500506 Audience Tertiary & Higher Education Country of Origin US Product Class Description Science & Mathematics: Textbooks & Study Guides AU Release Date 2001-04-26
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