Author | Ebbinghaus, Heinz-Dieter. author |
---|---|

Title | Finite Model Theory [electronic resource] / by Heinz-Dieter Ebbinghaus, Jรถrg Flum |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1995 |

Edition | Second Revised and Enlarged Edition 1999 |

Connect to | http://dx.doi.org/10.1007/3-540-28788-4 |

Descript | XIII, 362 p. online resource |

SUMMARY

Finite model theory, the model theory of finite structures, has roots in clasยญ sical model theory; however, its systematic development was strongly influยญ 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

CONTENT

Preliminaries -- The Ehrenfeucht-Fraรฏssรฉ Method -- More on Games -- 0-1 Laws -- Satisfiability in the Finite -- Finite Automata and Logic: A Microcosm of Finite Model Theory -- Descriptive Complexity Theory -- Logics with Fixed-Point Operators -- Logic Programs -- Optimization Problems -- Logics for PTIME -- Quantifiers and Logical Reductions

Mathematics
Mathematical logic
Mathematics
Mathematical Logic and Foundations
Mathematical Logic and Formal Languages