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Tuesday, November 27, 2018

**Abstract:** I will begin with a brief survey of model-theoretic tameness properties of some of the most natural abelian groups. Then I move on to describe our work where we consider two expansions each of groups of integers and rational numbers with a predicate for being square-free. We prove that one of the structures is model theoretically wild while the other three structures are model theoretically tame. Moreover, all these results can be seen as examples where number-theoretic randomness yields model-theoretic consequences. This is joint work with Minh Chieu Tran.