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Finite Model Theory

First Edition

  • Book
  • © 1995

Overview

Authors:
  1. Heinz-Dieter Ebbinghaus

    1. Institute of Mathematical Logic, University of Freiburg, Freiburg, Germany

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  2. Jörg Flum

    1. Institute of Mathematical Logic, University of Freiburg, Freiburg, Germany

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Perspectives in Mathematical Logic (PML)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XV
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  2. Preliminaries

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 1-12

  3. The Ehrenfeucht-Fraïssé Method

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 13-35

  4. More on Games

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 37-70

  5. 0–1 Laws

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 71-96

  6. Satisfiability in the Finite

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 97-105

  7. Finite Automata and Logic: A Microcosm of Finite Model Theory

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 107-118

  8. Descriptive Complexity Theory

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 119-163

  9. Logics with Fixed-Point Operators

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 165-234

  10. Logic Programs

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 235-264

  11. Optimization Problems

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 265-274

  12. Quantifiers and Logical Reductions

    • Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 275-311

  13. Back Matter

    Pages 313-327
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Keywords

About this book

Finite model theory has its origin in classical model theory, but owes its systematic development to research from complexity theory. The book presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed- point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. Other topics include DATALOG languages, quantifiers and oracles, 0-1 laws, and optimization and approximation problems. The book is written in such a way that the resp. parts on model theory and descriptive complexity theory may be read independently.

Reviews

"..a concise exposition that is at the same time comprehensive and lucid, providing good motivations and clear examples. The book can be thoroughly recommended for self-study and reference, or for an advanced course on this vital new subject." New Zealand Mathematical Society Newsletter

Authors and Affiliations

  • Institute of Mathematical Logic, University of Freiburg, Freiburg, Germany

    Heinz-Dieter Ebbinghaus, Jörg Flum

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