The Craig interpolation theorem in abstract model theory

Jouko Väänänen

pp. 401-420

in: Essays in honor of William Craig, Synthese 164 (3), 2008.

Abstract

The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics is small.