Infinitary Logic in Finite Model Theory

Abstract

The infinitary logic ℒ ω ∞ω consists of all formulas of ℒ∞ω with a finite number of variables. During the past several years, the study of ℒ ω ∞ω has occupied a prominent place in finite model theory. We present an overview of results concerning the interaction of ℒ ω ∞ω with least fixed-point logic and first-order implicit definability on finite structures.