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Mathematical Logic

An Introduction to Model Theory

  • Book
  • © 1978

Overview

Authors:
  1. A. H. Lightstone

    1. Queen’s University, Kingston, Canada

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    You can also search for this author in PubMed   Google Scholar

Editors:
  1. H. B. Enderton

    1. University of California, Los Angeles, USA

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

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    1. Introduction

      • A. H. Lightstone
      Pages 1-2

  3. Statement Systems and Propositional Calculus

    1. Front Matter

      Pages 3-3
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    2. Statement Systems

      • A. H. Lightstone
      Pages 5-9

    3. Propositional Calculus

      • A. H. Lightstone
      Pages 11-29

    4. Provable Wffs

      • A. H. Lightstone
      Pages 31-48

    5. Substitution Theorems

      • A. H. Lightstone
      Pages 49-56

    6. Duality

      • A. H. Lightstone
      Pages 57-73

    7. Deducibility and Completeness

      • A. H. Lightstone
      Pages 75-103

  4. Semantical Systems and Predicate Calculus

    1. Front Matter

      Pages 105-105
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    2. Semantical Systems

      • A. H. Lightstone
      Pages 107-128

    3. Predicate Calculus

      • A. H. Lightstone
      Pages 129-151

    4. Provable Wffs

      • A. H. Lightstone
      Pages 153-171

    5. Substitution Theorems

      • A. H. Lightstone
      Pages 173-182

    6. Duality

      • A. H. Lightstone
      Pages 183-200

    7. Deducibility and Completeness

      • A. H. Lightstone
      Pages 201-224

  5. Applications

    1. Front Matter

      Pages 225-225
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    2. Nonstandard Analysis

      • A. H. Lightstone
      Pages 227-262

    3. Normal Semantical Systems

      • A. H. Lightstone
      Pages 263-275

    4. Axiomatic Set Theory

      • A. H. Lightstone
      Pages 277-313
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Keywords

About this book

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.

Authors, Editors and Affiliations

  • University of California, Los Angeles, USA

    H. B. Enderton

  • Queen’s University, Kingston, Canada

    A. H. Lightstone

Bibliographic Information

  • Book Title: Mathematical Logic

  • Book Subtitle: An Introduction to Model Theory

  • Authors: A. H. Lightstone

  • Editors: H. B. Enderton

  • Series Title: Mathematical Concepts and Methods in Science and Engineering

  • DOI: https://doi.org/10.1007/978-1-4615-8750-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1978

  • Softcover ISBN: 978-1-4615-8752-1Published: 27 December 2012

  • eBook ISBN: 978-1-4615-8750-7Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XIII, 338

  • Topics: Mathematical Logic and Foundations

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