On the reducibility of isomorphism relations

TL;DR

This paper investigates the complexity of classifying models in the generalized Baire space, showing that for certain theories, isomorphism relations are reducible, revealing their relative complexity.

Contribution

It establishes a reducibility result between isomorphism relations of classifiable and stable theories with OCP in the context of inaccessible cardinals.

Findings

Isomorphism of models of classifiable theories reduces to that of stable theories with OCP.

The result applies specifically to inaccessible cardinals.

Provides insights into the hierarchy of classification problems in model theory.

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 $T'$.