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A counterexample on the reconstruction of oligomorphic clones Kompatscher, Michael


Two omega-categorical structures are first order bi-interpretable iff their automorphism groups are isomorphic as topological groups. For a lot of well-known omega-categorical structures this statement still holds if we ignore the topology. But in 1990 Evans and Hewitt constructed two omega-categorical structures with isomorphic, but not topologically isomorphic automorphism groups. Similarly two omega-categorical structures are primitive positive bi-interpretable iff their polymorphism clones are topologically isomorphic. Basing on the group-counterexample we were able to construct a counterexample for the clones. This is a joint work with Manuel Bodirsky, David Evans and Michael Pinsker.

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