Heinz-Dieter Ebbinghaus

Finite Automata and Logic: A Microcosm of Finite Model Theory

One of the major aims of finite model theory consists in characterizing the queries in a given complexity class by means of a logic in which they can be described. In this way one obtains a new measure of complexity: the complexity of formal descriptions. Moreover, the characterizations allow to translate problems on complexity classes into purely modeltheoretic problems, thus opening them to modeltheoretic methods. In general, this relationship between complexity classes and logics turns out to be useful for both, complexity theory and logic.

Zermelo: definiteness and the universe of definable sets

Using hitherto unpublished manuscripts from the Zermelo Nachlass, I describe the development of the notion of definiteness and the discussion about it, giving a conclusive picture of Zermelos thoughts up to the late thirties. As it turns out, Zermelos considerations about definiteness are intimately related to his concept of a Cantorian universe of categorically definable sets that may be considered an inner model of set theory in an ideationally given universe of classes.

Interpolation in Logiken monotoner systeme

AbstractA monotone structure (

Syntax der Sprachen erster Stufe

\mathfrak{A} ;

Die Sätze von Lindström

;μ) consists of a structure

Der Satz von Löwenheim und Skolem und der Endlichkeitssatz

\mathfrak{A}