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Course of Mathematical Logic

Volume 2 Model Theory

  • Book
  • © 1974

Overview

Authors:
  1. Roland Fraïssé
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Part of the book series: Synthese Library (SYLI, volume 69)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XIX
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  2. Local Isomorphism and Logical Formula; Logical Restriction Theorem

    • Roland Fraïssé
    Pages 1-29

  3. Logical Convergence; Compactness, Omission and Interpretability Theorems

    • Roland Fraïssé
    Pages 30-45

  4. Elimination of Quantifiers

    • Roland Fraïssé
    Pages 46-69

  5. Extension Theorems

    • Roland Fraïssé
    Pages 70-92

  6. Theories and Axiom Systems

    • Roland Fraïssé
    Pages 93-111

  7. Pseudo-Logical Class; Interpretability of Theories; Expansion of a Theory; Axiomatizability

    • Roland Fraïssé
    Pages 112-126

  8. Ultraproduct

    • Roland Fraïssé
    Pages 127-143

  9. Forcing

    • Roland Fraïssé
    Pages 144-157

  10. Isomorphisms and Equivalences in Relation to the Calculus of Infinitely Long Formulas with Finite Quantifiers

    • Roland Fraïssé
    Pages 158-178

  11. Back Matter

    Pages 179-197
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Keywords

About this book

This book is addressed primarily to researchers specializing in mathemat­ ical logic. It may also be of interest to students completing a Masters Degree in mathematics and desiring to embark on research in logic, as well as to teachers at universities and high schools, mathematicians in general, or philosophers wishing to gain a more rigorous conception of deductive reasoning. The material stems from lectures read from 1962 to 1968 at the Faculte des Sciences de Paris and since 1969 at the Universities of Provence and Paris-VI. The only prerequisites demanded of the reader are elementary combinatorial theory and set theory. We lay emphasis on the semantic aspect of logic rather than on syntax; in other words, we are concerned with the connection between formulas and the multirelations, or models, which satisfy them. In this context considerable importance attaches to the theory of relations, which yields a novel approach and algebraization of many concepts of logic. The present two-volume edition considerably widens the scope of the original [French] one-volume edition (1967: Relation, Formule logique, Compacite, Completude). The new Volume 1 (1971: Relation et Formule logique) reproduces the old Chapters 1, 2, 3, 4, 5 and 8, redivided as follows: Word, formula (Chapter 1), Connection (Chapter 2), Relation, operator (Chapter 3), Free formula (Chapter 4), Logicalformula,denumer­ able-model theorem (L6wenheim-Skolem) (Chapter 5), Completeness theorem (G6del-Herbrand) and Interpolation theorem (Craig-Lyndon) (Chapter 6), Interpretability of relations (Chapter 7).

Bibliographic Information

  • Book Title: Course of Mathematical Logic

  • Book Subtitle: Volume 2 Model Theory

  • Authors: Roland Fraïssé

  • Series Title: Synthese Library

  • DOI: https://doi.org/10.1007/978-94-010-2097-8

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1974

  • Hardcover ISBN: 978-90-277-0269-2Published: 31 October 1974

  • Softcover ISBN: 978-90-277-0510-5Published: 31 October 1974

  • eBook ISBN: 978-94-010-2097-8Published: 06 December 2012

  • Series ISSN: 0166-6991

  • Series E-ISSN: 2542-8292

  • Edition Number: 1

  • Number of Pages: XX, 198

  • Additional Information: Originally published in French

  • Topics: Logic, Mathematical Logic and Foundations

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