Recursion theory, Gödel's theorems, set theory, model theory
著者
書誌事項
Recursion theory, Gödel's theorems, set theory, model theory
（Mathematical logic : a course with exercises / René Cori and Daniel Lascar ; translated by Donald H. Pelletier, pt. 2）
Oxford University Press, 2001
- : hbk
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780198500506
内容説明
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 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.
目次
- Contents of Part I
- Notes from the translator
- Notes to the reader
- 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
- 巻冊次
-
: hbk ISBN 9780198500513
内容説明
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 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.
目次
- 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
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