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Finite Model Theory

  • Heinz-Dieter Ebbinghaus
  • Jörg Flum

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

Table of contents

  1. Front Matter
    Pages I-XV
  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 37-70
  5. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 71-96
  6. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 97-105
  7. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 107-118
  8. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 119-163
  9. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 165-234
  10. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 235-264
  11. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 265-274
  12. Heinz-Dieter Ebbinghaus, Jörg Flum
    Pages 275-311
  13. Back Matter
    Pages 313-327

About this book

Introduction

Finite model theory has its origins 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.

Keywords

0-1-Gesetze 0-1-laws Deskriptive Komplexitätstheorie Fixpunktlogiken automata boolean satisfiability problem complexity complexity theory description complexity theory finite model theory fixed-point logics logic model theory optimization theory of complexity

Authors and affiliations

  • Heinz-Dieter Ebbinghaus
    • 1
  • Jörg Flum
    • 1
  1. 1.Institute of Mathematical LogicUniversity of FreiburgFreiburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03182-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-03184-1
  • Online ISBN 978-3-662-03182-7
  • Series Print ISSN 0172-6641
  • Buy this book on publisher's site
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