Minimal models of minimal theories
The author proves that a first-order theory, \(T\), has \(2^{\aleph_ 0}\) minimal models, if it is stable and trivial, and if it has a minimal and non-prime model in which each element has Lascar rank \(\leq 1\). This result is valid for any language in contrast to Marcus's and Toffalori's works that consider the language with one unary function [cf. \textit{L. Marcus}, Isr. J. Math. 18, 117-131 (1974; Zbl 0298.02059), and \textit{C. Toffalori}, Ill. J. Math. 35, No. 1, 1-26 (1991; Zbl 0696.03018), respectively]. The author shows that their example satisfies the assumptions of the above theorem as well as \textit{G. Fuhrken's} [Arch. Math. Logik Grundlagenforsch. 9, 3-11 (1966; Zbl 0168.007)]. On the other hand, \textit{S. Shelah's} do not, as all minimal models there have Lascar rank 2 [cf. J. Symb. Log. 43, 475-480 (1978; Zbl 0389.03014)].
scientific article; zbMATH DE number 591460