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Introduction to Mathematical Logic Set Theory Computable Functions Model Theory

This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere­ quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in provid...

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Bibliographic Details
Main Author: Malitz, Jerome
Format: eBook
Language:English
Published: New York, NY Springer New York 1979, 1979
Edition:1st ed. 1979
Series:Undergraduate Texts in Mathematics
Subjects:
Mathematical Logic
Mathematical Logic And Foundations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I: An Introduction to Set Theory
  • 1.1 Introduction
  • 1.2 Sets
  • 1.3 Relations and Functions
  • 1.4 Pairings
  • 1.5 The Power Set
  • 1.6 The Cantor-Bernstein Theorem
  • 1.7 Algebraic and Transcendental Numbers
  • 1.8 Orderings
  • 1.9 The Axiom of Choice
  • 1.10 Transfinite Numbers
  • 1.11 Paradise Lost, Paradox Found (Axioms for Set Theory)
  • 1.12 Declarations of Independence
  • II: An Introduction to Computability Theory
  • 2.1 Introduction
  • 2.2 Turing Machines
  • 2.3 Etemonstrating Computability without an Explicit Description of a Turing Machine
  • 2.4 Machines for Composition, Recursion, and the “Least Operator”
  • 2.5 Of Men and Machines
  • 2.6 Non-computable Functions
  • 2.7 Universal Machines
  • 2.8 Machine Enumerabihty
  • 2.9 An Alternate Definition of Computable Function
  • 2.10 An Idealized Language
  • 2.11 Definabihty in Arithmetic
  • 2.12 The Decision Problem for Arithmetic
  • 2.13 Axiomatizing Arithmetic
  • 2.14 Some Directions in Current Research
  • III: An Introduction to Model Theory
  • 3.1 Introduction
  • 3.2 The First Order Predicate Calculus
  • 3.3 Structures
  • 3.4 Satisfaction and Truth
  • 3.5 Normal Forms
  • 3.6 The Compactness Theorem
  • 3.7 Proof of the Compactness Theorem
  • 3.8 The Lowenheim-Skolem Theorem
  • 3.9 The Prefix Problem
  • 3.10 Interpolation and Definabihty
  • 3.11 Herbrand’s Theorem
  • 3.12 Axiomatizing the Validities of L
  • 3.13 Some Recent Trends in Model Theory

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