\(\omega\)-stable structures of small CB-rank (Q1097874)

Let T be a countable complete \(\omega\)-stable theory. The CB-spectrum of T is the set S, ordered lexicographically, of all pairs \((a_ M,d_ M)\) where \(a_ M\) and \(d_ M\) are respectively the CB-rank and CB-degree of \(v=v\) in the countable model M of T (CB stands for Cantor-Bendixson). This paper deals with the classification of the T's whose minimal element of S is (2,1) (the case where it was (1,-) was studied in previous papers by the author and A. Marcja). An ``almost complete'' classification of \(\omega\)-stable groups and rings whose CB-spectra contains (2,1) (which is then minimal) is given (the classification of groups follows from the author's remark that Cherlin's classification of groups of Morley rank- degree (2,1) goes through under the weaker hypothesis here). In the second part the author explores the general T's such that \((2,1)=\min S\) or \(S=\{(2,1)\}\).