Editing Model theory (section)

===Finite model theory ===

{{main|Finite model theory}}
[[Finite model theory]], which concentrates on finite structures, diverges significantly from the study of infinite structures in both the problems studied and the techniques used.<ref>{{Cite book|last1=Ebbinghaus|first1=Heinz-Dieter|last2=Flum|first2=Jörg|date=1995|title=Finite Model Theory|url=http://dx.doi.org/10.1007/978-3-662-03182-7|series=Perspectives in Mathematical Logic|doi=10.1007/978-3-662-03182-7|page=v|isbn=978-3-662-03184-1}}</ref> In particular, many central results of classical model theory that fail when restricted to finite structures. This includes the [[compactness theorem]], [[Gödel's completeness theorem]], and the method of [[ultraproducts]] for [[first-order logic]]. At the interface of finite and infinite model theory are algorithmic or [[computable model theory]] and the study of [[Zero-one law (model theory)|0-1 laws]], where the infinite models of a generic theory of a class of structures provide information on the distribution of finite models.<ref>{{Cite book|last1=Ebbinghaus|first1=Heinz-Dieter|last2=Flum|first2=Jörg|date=1995|title=Finite Model Theory|url=http://dx.doi.org/10.1007/978-3-662-03182-7|series=Perspectives in Mathematical Logic|doi=10.1007/978-3-662-03182-7|chapter=0-1 Laws|isbn=978-3-662-03184-1}}</ref> 
Prominent application areas of FMT are [[descriptive complexity theory]], [[database theory]] and [[formal language theory]].<ref>{{Cite book|last1=Ebbinghaus|first1=Heinz-Dieter|last2=Flum|first2=Jörg|date=1995|title=Finite Model Theory|url=http://dx.doi.org/10.1007/978-3-662-03182-7|series=Perspectives in Mathematical Logic|doi=10.1007/978-3-662-03182-7|isbn=978-3-662-03184-1}}</ref>