Finite Model Theory

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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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.

• 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
• algorithm analysis and problem complexity

"..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

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

  Heinz-Dieter Ebbinghaus, Jörg Flum