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Finite Model Theory

  • Heinz-Dieter Ebbinghaus
  • Jörg Flum

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 1-12
  3. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 13-35
  4. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 37-69
  5. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 71-93
  6. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 95-103
  7. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 105-117
  8. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 119-164
  9. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 165-238
  10. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 239-273
  11. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 275-285
  12. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 287-306
  13. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 307-338
  14. Back Matter
    Pages 339-360

About this book

Introduction

Finite model theory, the model theory of finite structures, has roots in clas­ sical model theory; however, its systematic development was strongly influ­ enced by research and questions of complexity theory and of database theory. Model theory or the theory of models, as it was first named by Tarski in 1954, may be considered as the part of the semantics of formalized languages that is concerned with the interplay between the syntactic structure of an axiom system on the one hand and (algebraic, settheoretic, . . . ) properties of its models on the other hand. As it turned out, first-order language (we mostly speak of first-order logic) became the most prominent language in this respect, the reason being that it obeys some fundamental principles such as the compactness theorem and the completeness theorem. These principles are valuable modeltheoretic tools and, at the same time, reflect the expressive weakness of first-order logic. This weakness is the breeding ground for the freedom which modeltheoretic methods rest upon. By compactness, any first-order axiom system either has only finite models of limited cardinality or has infinite models. The first case is trivial because finitely many finite structures can explicitly be described by a first-order sentence. As model theory usually considers all models of an axiom system, modeltheorists were thus led to the second case, that is, to infinite structures. In fact, classical model theory of first-order logic and its generalizations to stronger languages live in the realm of the infinite.

Keywords

0-1-laws Finite model theory complexity complexity theory descriptive complexity theory fixed-point logics model theory

Authors and affiliations

  • Heinz-Dieter Ebbinghaus
    • 1
  • Jörg Flum
    • 1
  1. 1.Mathematisches Institut Abteilung für Mathematische LogikUniversität FreiburgFreiburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-28788-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-28787-2
  • Online ISBN 978-3-540-28788-9
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site
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