CONTINUOUS LOGIC AND BOREL EQUIVALENCE RELATIONS
CONTINUOUS LOGIC AND BOREL EQUIVALENCE RELATIONS
Abstract We study the complexity of isomorphism of classes of metric structures using methods from infinitary continuous logic. For Borel classes of locally compact structures, we prove that if the equivalence relation of isomorphism is potentially $\mathbf {\Sigma }^0_2$ , then it is essentially countable. We also provide an equivalent …