Mathematical Logic

An Introduction to Model Theory

  • A. H. Lightstone
  • H. B. Enderton

Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 9)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Introduction

    1. A. H. Lightstone
      Pages 1-2
  3. Statement Systems and Propositional Calculus

    1. Front Matter
      Pages 3-3
    2. A. H. Lightstone
      Pages 5-9
    3. A. H. Lightstone
      Pages 11-29
    4. A. H. Lightstone
      Pages 31-48
    5. A. H. Lightstone
      Pages 49-56
    6. A. H. Lightstone
      Pages 57-73
    7. A. H. Lightstone
      Pages 75-103
  4. Semantical Systems and Predicate Calculus

    1. Front Matter
      Pages 105-105
    2. A. H. Lightstone
      Pages 107-128
    3. A. H. Lightstone
      Pages 129-151
    4. A. H. Lightstone
      Pages 153-171
    5. A. H. Lightstone
      Pages 173-182
    6. A. H. Lightstone
      Pages 183-200
    7. A. H. Lightstone
      Pages 201-224
  5. Applications

    1. Front Matter
      Pages 225-225
    2. A. H. Lightstone
      Pages 227-262
    3. A. H. Lightstone
      Pages 263-275
    4. A. H. Lightstone
      Pages 277-313

About this book

Introduction

Before his death in March, 1976, A. H. Lightstone delivered the manu­ script for this book to Plenum Press. Because he died before the editorial work on the manuscript was completed, I agreed (in the fall of 1976) to serve as a surrogate author and to see the project through to completion. I have changed the manuscript as little as possible, altering certain passages to correct oversights. But the alterations are minor; this is Lightstone's book. H. B. Enderton vii Preface This is a treatment of the predicate calculus in a form that serves as a foundation for nonstandard analysis. Classically, the predicates and variables of the predicate calculus are kept distinct, inasmuch as no variable is also a predicate; moreover, each predicate is assigned an order, a unique natural number that indicates the length of each tuple to which the predicate can be prefixed. These restrictions are dropped here, in order to develop a flexible, expressive language capable of exploiting the potential of nonstandard analysis. To assist the reader in grasping the basic ideas of logic, we begin in Part I by presenting the propositional calculus and statement systems. This provides a relatively simple setting in which to grapple with the some­ times foreign ideas of mathematical logic. These ideas are repeated in Part II, where the predicate calculus and semantical systems are studied.

Keywords

Apple Calc Mathematica Natural Tuple calculus form language logic mathematical logic proof proposition set theory variable

Authors and affiliations

  • A. H. Lightstone
    • 1
  1. 1.Queen’s UniversityKingstonCanada

Editors and affiliations

  • H. B. Enderton
    • 1
  1. 1.University of CaliforniaLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-8750-7
  • Copyright Information Springer-Verlag US 1978
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4615-8752-1
  • Online ISBN 978-1-4615-8750-7
  • About this book