Vaught's conjecture for some meager groups (Q1806723)

The author investigates meager groups \(G\) of \({\mathcal M}\)-rank 1, and in some cases proves Vaught's conjecture for Th\((G)\). In particular, he proves that if that group \(G\) is of \(U\)-rank \(\omega\) and the ring \(F_G\) of pseudo-endomorphisms of \(G\) is a prime field, then Vaught's conjecture holds for TH\((G)\). The proof is an application of the techniques of meager types, calculus of traces of types and \(Q\)-isolation, developed in earlier papers of the author.