The isomorphism relation of theories with S-DOP in generalized Baire spaces

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 $T^{\prime }$ is superstable with the strong dimensional order property (S-DOP), then the isomorphism of models of $T$ is Borel reducible to the isomorphism of models of $T^{\prime }$. In fact we show the consistency of the following: If $\kappa$ is inaccessible and $T$ is a superstable theory with S-DOP, then the isomorphism of models of $T$ is ${\Sigma }_1^1$-complete.

References in corpus (2)

• Generalized Descriptive Set Theory and Classification Theory
• On Local Club Condensation

Cited by in corpus (1)

• On unsuperstable theories in GDST