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  1. Weak elimination of imaginaries for Boolean algebras.Roman Wencel - 2005 - Annals of Pure and Applied Logic 132 (2-3):247-270.
    We give a complete characterization of Boolean algebras admitting weak elimination of imaginaries in terms of elementary invariants.
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  • Imaginaries in Boolean algebras.Roman Wencel - 2012 - Mathematical Logic Quarterly 58 (3):217-235.
    Given an infinite Boolean algebra B, we find a natural class of equation image-definable equivalence relations equation image such that every imaginary element from Beq is interdefinable with an element from a sort determined by some equivalence relation from equation image. It follows that B together with the family of sorts determined by equation image admits elimination of imaginaries in a suitable multisorted language. The paper generalizes author's earlier results concerning definable equivalence relations and weak elimination of imaginaries for Boolean (...)
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  • 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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