Structures coordinatized by indiscernible sets (Q1109025)

The paper studies countable \(\aleph_ 0\)-stable, \(\aleph_ 0\)- categorical structures M which satisfy: any strictly minimal set definable in \(M^{eq}\) is indescernible. In particular, it is shown that each such structure admits a finite language and is uniformly explicitly definable from a countable linear ordering. The author conjectures that some of the results proved for this class of structures will turn out to be true for the broader class of countable \(\aleph_ 0\)-stable, \(\aleph_ 0\)-categorical structures.