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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.

MSC:

03C64 Model theory of ordered structures; o-minimality
03C35 Categoricity and completeness of theories
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