Part 2: Recursion Theory, Godel's Theorems, Set Theory, Model Theory - Rilegato

Cori, René; Lascar, Daniel

 
9780198500513: Part 2: Recursion Theory, Godel's Theorems, Set Theory, Model Theory
Rilegato
ISBN 10: 0198500513 ISBN 13: 9780198500513
Casa editrice: OUP Oxford, 2001

Sinossi

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

L'autore

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.

Contenuti

  • 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

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
OUP Oxford
Data di pubblicazione
2001
Lingua
Inglese
ISBN 10 
0198500513
ISBN 13 
9780198500513
Rilegatura
Copertina rigida
Numero di pagine
352
Contatto del produttore
Messaggerie Libri
ufficio.anagrafiche@meli.it

Via Verdi, 8.
Assago Milano
20090
Italia

Altre edizioni note dello stesso titolo

9780198500506: Recursion Theory, Godel's Theorems, Set Theory, Model Theory (Mathematical Logic: A Course With Exercises, Part II)

Edizione in evidenza

ISBN 10:  0198500505 ISBN 13:  9780198500506
Casa editrice: Oxford University Press, USA, 2001
Brossura