E-Books →Finite Model Theory

Free Download Finite Model Theory By Heinz-Dieter Ebbinghaus, Jörg Flum
1995 | 336 Pages | ISBN: 3662031841 | PDF | 26 MB
This is the first edition. The second edition was published in the "Springer Monographs in Mathematics" series in 2005.The branch of model theory described in the present book and called finitemodel theory has its roots in classical model theory but owes its systematicdevelopment to research from complexity theory.Model theory or the theory of models, as it was first named by Tarski in1954, may be considered as the part of the semantics of f.Qrmalized languagesthat is concerned with the interplay between the syntactic structure of anaxiom system on the one hand and (algebraic, set-theoretic, ... ) propertiesof its models on the other hand. As it turned out, first-order language (wemostly speak of first-order logic) became the most prominent language in thisrespect, the reason being that it obeys some fundamental principles such asthe compactness theorem and the completeness theorem. These principles arevaluable modeltheoretic tools and, at the same time, reflect the expressiveweakness of first-order logic. This weakness is the breeding ground for thefreedom which modeltheoretic methods rest upon.