We'll pick up where we left off, discussing the connections between Borel spaces of countable structures and the infinitary logic Lω1ω. The Lopez-Escobar theorem says that a class of countable structures is isomorphism-invariant & Borel iff it's axiomatizable by an Lω1ω-sentence. What about ≅-equivariant Borel maps? These correspond to "Lω1ω-interpretations", which can be thought of as recipes for constructing different types of structures from each other. We'll discuss the space of infinitary theories ordered by interpretability. Then we'll describe the notion of 'structurability', through which we can see that many constructions in the theory of countable Borel equivalence relations (CBERs) are naturally phrased in terms of interpretations. Time permitting, we'll describe a close correspondence between the set of theories (ordered by interpretability) and the set of CBERs (ordered by class-bijective Borel homomorphisms).