# López-Escobar's theorem for metric structures

Boise Set Theory Seminar, Boise, April 2015

*Abstract*: The classical López-Escobar theorem states that any Borel class of countable structures may be axiomatized using an appropriate infinitary logic. One application of this theorem is to relate topological and model-theoretic versions of Vaught’s conjecture. In this talk we present a variant of López-Escobar’s theorem for metric structures, which implies that Borel classes of separable metric structures may be axiomatized in the appropriate infinitary continuous logic. As a consequence we obtain a new implication between the topological Vaught conjecture and a version for metric structures. This is joint work with Martino Lupini.