Kulpeshov, B. Sh. Definable functions in the \(\aleph_0\)-categorical weakly circularly minimal structures. (Russian, English) Zbl 1224.03017 Sib. Mat. Zh. 50, No. 2, 356-379 (2009); translation in Sib. Math. J. 50, No. 2, 282-301 (2009). Summary: We continue studying the analogs of o-minimality and weak o-minimality for circularly ordered sets. We present a complete characterization of the behavior of unary definable functions in an \(\aleph_0\)-categorical 1-transitive weakly circularly minimal structure. Using it, we describe the \(\aleph_0\)-categorical 1-transitive nonprimitive weakly circularly minimal structures of convexity rank greater than 1 up to binarity. Cited in 5 Documents MSC: 03C64 Model theory of ordered structures; o-minimality 03C35 Categoricity and completeness of theories Keywords:circularly ordered set; weak circular minimality; categoricity; convexity rank PDFBibTeX XMLCite \textit{B. Sh. Kulpeshov}, Sib. Mat. Zh. 50, No. 2, 356--379 (2009; Zbl 1224.03017); translation in Sib. Math. J. 50, No. 2, 282--301 (2009) Full Text: EuDML EMIS