This article is cited in 10 papers

Definable functions in the $\aleph_0$-categorical weakly circularly minimal structures

B. Sh. Kulpeshov

Institute for Problems of Informatics and Control Sciences, Almaty, Kazhakhstan

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 $\aleph_0$-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.

Keywords: circularly ordered set, weak circular minimality, $\aleph_0$-categoricity, convexity rank.

UDC: 510.67

Received: 06.09.2007

 English version: Siberian Mathematical Journal, 2009, 50:2, 282–301

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