Rene Cori, Daniel Lascar, Ren? Cori

Mathematical Logic

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

• Gebundenes Buch

Produktbeschreibung

The requirement to reason logically forms the basis of all mathematics, and hence mathematical logic is one of the most fundamental topics that students study. Assuming no prior knowledge of the topic, this book provides an introduction for advanced undergraduate students. The concept of model underlies the text, giving it a theoretical coherence.

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Produktdetails

• Verlag: Hurst & Co.
• Seitenzahl: 352
• Erscheinungstermin: 21. Juni 2001
• Englisch
• Abmessung: 234mm x 156mm x 21mm
• Gewicht: 667g
• ISBN-13: 9780198500513
• ISBN-10: 0198500513
• Artikelnr.: 24077268

Inhaltsangabe

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