On the reducibility of isomorphism relations

Abstract: We study the Borel reducibility of isomorphism relations in the generalized Baire space $\kappa^\kappa$. In the main result we show for inaccessible $\kappa$, that if $T$ is a classifiable theory and $T'$ is stable with OCP, then the isomorphism of models of $T$ is Borel reducible to the isomorphism of models of $T'$.