Abstract
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 ℵ0-categorical 1-transitive weakly circularly minimal structure. Using it, we describe the ℵ0-categorical 1-transitive nonprimitive weakly circularly minimal structures of convexity rank greater than 1 up to binarity.
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References
Kulpeshov B. Sh. and Macpherson H. D., “Minimality conditions on circularly ordered structures,” Math. Logic Quart., 51, No. 4, 377–399 (2005).
Kulpeshov B. Sh., “On ℵ0-categorical weakly circularly minimal structures,” Math. Logic Quart., 52, No. 6, 555–574 (2006).
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Original Russian Text Copyright © 2009 Kupleshov B. Sh.
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Almaty. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 356–379, March–April, 2009.
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Kulpeshov, B.S. Definable functions in the ℵ0-categorical weakly circularly minimal structures. Sib Math J 50, 282–301 (2009). https://doi.org/10.1007/s11202-009-0034-3
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DOI: https://doi.org/10.1007/s11202-009-0034-3