Some combinatorial aspects of the cover problem for totally categorical theories
А. А. Иванов · 1994
Abstract A finite cover M of a structure N is obtained in the following way. For a finite set F consider a structure M = NU (N ×F) with the natural projection π from N ×F onto N. Some new relations may be added to M but no new structure is induced on N. In this paper we usually assume that N is a strictly minimal countably categorical set. Such covers appear in the investigation of totally categorical theories and the problem of a description of them seems very difficult. We approach this ‘cover problem’ by analysing arities of covers. Mainly, we are interested in what covers can be obtained by adding binary relations to principal finite covers. We show that these covers split and in some natural situations they can be characterized completely.