Mathematical Logic: A Course with Exercises Part 2: Recursion Theory, Godels Theorems, Set Theory…

Paperback | April 1, 2001

byRene Cori, Daniel LascarTranslated byDonald Pelletier

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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 andprovides 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 topicessential 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 theappendix.

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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 andprovides a clear and accessible introductio...

Rene Cori is at Universite Paris VII. Daniel Lascar is at Universite Paris VII. Donald Pelletier is at York University, Toronto and Universite Paris VII.

other books by Rene Cori

Mathematical Logic: A Course With Exercises Part 1: Propositional Calculus, Boolean Algebras…
Mathematical Logic: A Course With Exercises Part 1: Pro...

Paperback|Jun 15 2000

$127.16 online$165.00list price(save 22%)
Format:PaperbackDimensions:352 pages, 9.21 × 6.14 × 0.75 inPublished:April 1, 2001Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198500505

ISBN - 13:9780198500506

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Table of Contents

Contents 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, Godel'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

Editorial 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 (bothU. 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 aresolutions!"The Bulletin of Mathematics Books