Abstract: 

Notions of reducibility between various kinds of structures play an important role in mathematical logic, especially in set theory and computability theory. Examples include Borel and Turing reducibility. However, the only model-theoretic notion of reducibility that I am aware of is interpretability, which is rather rigid. We introduce a novel notion of model-theoretic reducibility and discuss a recently developed connection with constraint satisfaction problems. Along the way we will attempt to convince the audience that the trivial theory of an infinite set with equality is surprisingly interesting.

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