Rene Cori, Daniel Lascar, Ren? Cori

Mathematical Logic

A Course with Exercises Part II: Recursion Theory, Godel's Theorems, Set Theory, Model Theory

• Broschiertes Buch

Produktbeschreibung

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.

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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.

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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Verlag: OUP Oxford
• Seitenzahl: 352
• Erscheinungstermin: 12. April 2001
• Englisch
• Abmessung: 234mm x 156mm x 20mm
• Gewicht: 535g
• ISBN-13: 9780198500506
• ISBN-10: 0198500505
• Artikelnr.: 21532809

Inhaltsangabe

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, Gödel'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