Mathematical Logic: Part 2
Recursion Theory, Godel's Theorems, Set Theory, Model Theory
Published on 12. April 2001
Book
Hardback
352 pages
978-0-19-850051-3 (ISBN)
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 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.
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Target group
College/higher education
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 23 mm
Weight
693 gr
ISBN-13
978-0-19-850051-3 (9780198500513)
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Schweitzer Classification
Other editions
Additional editions
Rene Cori | Daniel Lascar
Mathematical Logic: Part 2
Recursion Theory, Godel's Theorems, Set Theory, Model Theory
Book
04/2001
Oxford University Press
€129.60
Shipment within 15-20 days
Persons
Content
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