Ehrenfeucht theories without powerful digraphs*

Abstract

All Ehrenfeucht theories are based on digraphs having the local pairwise intersection property. In this case, all known Ehrenfeucht theories are based on digraphs having the global pairwise intersection property. In the paper, we construct examples of Ehrenfeucht theories with powerful digraphs having the local pairwise intersection property, without the global pairwise intersection property, and thus without powerful digraphs.