Fixpoint logic vs. infinitary logic in finite-model theory

Abstract

The relationship between fixpoint logic and the infinitary logic L/sub infinity omega //sup omega / with a finite number of variables is studied. It is observed that the equivalence of two finite structures with respect to L/sub infinity omega //sup omega / is expressible in fixpoint logic. As a first application of this, a normal-form theorem for L infinity /sub omega //sup omega / on finite structures is obtained. The relative expressive power of first-order logic, fixpoint logic, and L/sub infinity omega //sup omega / on arbitrary classes of finite structures is examined. A characterization of when L/sub infinity omega //sup omega / collapses to first-order logic on an arbitrary class of finite structures is given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>