An Ehrenfeucht‐Fraïssé game for

Abstract

In this paper we develop an Ehrenfeucht‐Fraïssé game for . Unlike the standard Ehrenfeucht‐Fraïssé games which are modeled solely after the behavior of quantifiers, this new game also takes into account the behavior of connectives in logic. We prove the adequacy theorem for this game. We also apply the new game to prove complexity results about infinite binary strings.