Finite model theory.

Finite model theory.

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Bibliographic Details
Author / Creator:Ebbinghaus, Heinz-Dieter, 1939-
Edition:2nd ed.
Imprint:Berlin ; New York : Springer, c2006.
Description:xi, 360 p. ; 24 cm.
Language:English
Series:Springer monographs in mathematics
Subject:
Model theory.
Model theory.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/5786602
Hidden Bibliographic Details
Other authors / contributors:Flum, Jörg.
ISBN:3540287876
Table of Contents:
  • Preface
  • 1. Preliminaries
  • 2. The Ehrenfeucht-Fraisse Method
  • 2.1. Elementary Classes
  • 2.2. Ehrenfeucht's Theorem
  • 2.3. Examples and Fraisse's Theorem
  • 2.4. Hanf's Theorem
  • 2.5. Gaifman's Theorem
  • 3. More on Games
  • 3.1. Second-Order Logic
  • 3.2. Infinitary Logic: The Logics L[subscript infinity omega] and L[subscript [omega]1[omega]]
  • 3.3. The Logics FO[superscript s] and L[superscript s subscript infinity omega]
  • 3.3.1. Pebble Games
  • 3.3.2. The s-Invariant of a Structure
  • 3.3.3. Scott Formulas
  • 3.4. Logics with Counting Quantifiers
  • 3.5. Failure of Classical Theorems in the Finite
  • 4. 0-1 Laws
  • 4.1. 0-1 Laws for FO and L[superscript omega subscript infinity omega]
  • 4.2. Parametric Classes
  • 4.3. Unlabeled 0-1 Laws
  • 4.3.1. Appendix
  • 4.4. Examples and Consequences
  • 4.5. Probabilities of Monadic Second Order Properties
  • 5. Satisfiability in the Finite
  • 5.1. Finite Model Property of FO[superscript 2]
  • 5.2. Finite Model Property of [characters not reproducible]-Sentences
  • 6. Finite Automata and Logic: A Microcosm of Finite Model Theory
  • 6.1. Languages Accepted by Automata
  • 6.2. Word Models
  • 6.3. Examples and Applications
  • 6.4. First-Order Definability
  • 7. Descriptive Complexity Theory
  • 7.1. Some Extensions of First-Order Logic
  • 7.2. Turing Machines and Complexity Classes
  • 7.2.1. Digression: Trahtenbrot's Theorem
  • 7.2.2. Structures as Inputs
  • 7.3. Logical Descriptions of Computations
  • 7.4. The Complexity of the Satisfaction Relation
  • 7.5. The Main Theorem and Some Consequences
  • 7.5.1. Appendix
  • 8. Logics with Fixed-Point Operators
  • 8.1. Inflationary and Least Fixed-Points
  • 8.2. Simultaneous Induction and Transitivity
  • 8.3. Partial Fixed-Point Logic
  • 8.4. Fixed-Point Logics and L[superscript omega subscript infinity omega]
  • 8.4.1. The Logic FO(PFP[subscript PTIME])
  • 8.4.2. Fixed-Point Logic with Counting
  • 8.5. Fixed-Point Logics and Second-Order Logic
  • 8.5.1. Digression: Implicit Definability
  • 8.6. Transitive Closure Logic
  • 8.6.1. FO(DTC)
  • 8.6.2. FO(posTC) and Normal Forms
  • 8.6.3. FO(TC)
  • 8.7. Bounded Fixed-Point Logic
  • 9. Logic Programs
  • 9.1. DATALOG
  • 9.2. I-DATALOG and P-DATALOG
  • 9.3. A Preservation Theorem
  • 9.4. Normal Forms for Fixed-Point Logics
  • 9.5. An Application of Negative Fixed-Point Logic
  • 9.6. Hierarchies of Fixed-Point Logics
  • 10. Optimization Problems
  • 10.1. Polynomially Bounded Optimization Problems
  • 10.2. Approximable Optimization Problems
  • 11. Logics for PTIME
  • 11.1. Logics and Invariants
  • 11.2. PTIME on Classes of Structures
  • 12. Quantifiers and Logical Reductions
  • 12.1. Lindstrom Quantifiers
  • 12.2. PTIME and Quantifiers
  • 12.3. Logical Reductions
  • 12.4. Quantifiers and Oracles
  • References
  • Index

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