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Springer Monographs in Mathematics Ser.: Finite Model Theory by Heinz-Dieter Ebbinghaus and Jörg Flum (2005, Hardcover)
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About this product
Product Identifiers
PublisherSpringer Berlin / Heidelberg
ISBN-103540287876
ISBN-139783540287872
eBay Product ID (ePID)49203001
Product Key Features
Number of PagesXi, 360 Pages
Publication NameFinite Model Theory
LanguageEnglish
Publication Year2005
SubjectComputer Science, Logic
FeaturesRevised
TypeTextbook
Subject AreaMathematics, Computers
AuthorHeinz-Dieter Ebbinghaus, Jörg Flum
SeriesSpringer Monographs in Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.4 in
Item Weight54.7 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
LCCN2005-932862
Dewey Edition22
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal511.3/4
Table Of ContentPreliminaries.- The Ehrenfeucht-Fraïssé 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.
Edition DescriptionRevised edition
SynopsisThis volume presents the main results of descriptive complexity theory: the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. Important logics in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages. 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 respective parts on model theory and descriptive complexity theory may be read independently. This second edition is a thoroughly revised and enlarged version of the original text., Finite model theory, the model theory of finite structures, has roots in clas- sical model theory; however, its systematic development was strongly influ- 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., Finite model theory, the model theory of finite structures, has roots in clas sical model theory; however, its systematic development was strongly influ 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., Finite model theory, the model theory of finite structures, has roots in clas sical model theory; however, its systematic development was strongly influ 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 freedomwhich 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.
LC Classification NumberQA8.9-10.3
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