Siberian Mathematical Journal

, Volume 50, Issue 2, pp 282–301

Definable functions in the ℵ0-categorical weakly circularly minimal structures

Article

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.

Keywords

circularly ordered set weak circular minimality 0-categoricity convexity rank 

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References

  1. 1.
    Kulpeshov B. Sh. and Macpherson H. D., “Minimality conditions on circularly ordered structures,” Math. Logic Quart., 51, No. 4, 377–399 (2005).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Kulpeshov B. Sh., “On ℵ0-categorical weakly circularly minimal structures,” Math. Logic Quart., 52, No. 6, 555–574 (2006).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Informatics and Control Problems Institute AlmatyKazakhstanRussia

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