The Ehrenfeucht-Fraïssé Method

The Ehrenfeucht-Fraisse method is among the few tools of model theory that survive when we restrict our attention to finite structures. We present the method in its gametheoretic, its algebraic, and its logical form (due to Ehrenfeucht, Fraisse, and Hintikka, respectively). Later we shall see that generalizations are also available for some extensions of first-order logic. The detailed presentation for the case of first-order logic will help to understand these extensions, where in each case we only will indicate the changes that are necessary.