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Springer Monographs in Mathematics

Finite Model Theory

Second Edition

Authors: Ebbinghaus, Heinz-Dieter, Flum, Jörg

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About this book

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.

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook 117,69 €
price for Spain (gross)
  • ISBN 978-3-540-28788-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 145,59 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Finite Model Theory
Book Subtitle
Second Edition
Authors
Series Title
Springer Monographs in Mathematics
Copyright
1995
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-28788-9
DOI
10.1007/3-540-28788-4
Hardcover ISBN
978-3-540-28787-2
Series ISSN
1439-7382
Edition Number
2
Number of Pages
XI, 360
Additional Information
Originally published in the series: Perspectives in Mathematical Logic
Topics