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A counterexample on the reconstruction of oligomorphic clones

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Combinatorics; Dynamical systems and ergodic theory; Logic and foundations

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Author affiliation: Vienna University of Technology

2016-05-14

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58146

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/