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  1.  9
    Minimality Conditions on Circularly Ordered Structures.Beibut Sh Kulpeshov & H. Dugald Macpherson - 2005 - Mathematical Logic Quarterly 51 (4):377-399.
    We explore analogues of o-minimality and weak o-minimality for circularly ordered sets. Much of the theory goes through almost unchanged, since over a parameter the circular order yields a definable linear order. Working over ∅ there are differences. Our main result is a structure theory for ℵ0-categorical weakly circularly minimal structures. There is a 5-homogeneous example which is not 6-homogeneous, but any example which is k-homogeneous for some k ≥ 6 is k-homogeneous for all k.
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  2.  6
    Metrically Homogeneous Graphs of Diameter Three.Daniela Amato, Gregory Cherlin & H. Dugald Macpherson - forthcoming - Journal of Mathematical Logic.
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    Metrically Homogeneous Graphs of Diameter 3.Daniela A. Amato, Gregory Cherlin & H. Dugald Macpherson - 2020 - Journal of Mathematical Logic 21 (1):2050020.
    We classify countable metrically homogeneous graphs of diameter 3.
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