Fodor space in generalized descriptive set theory

Abstract

We study the continuous reducibility of isomorphism relations in the space of regresive functions in $\hat{I}{º}^{\hat{I}}º$. We show for inaccessible $\hat{I}º$, that if $\mathcal{T}$ is a theory with less than $\hat{I}º$ non-isomorphic models of size $\hat{I}º$ and ${\mathcal{T}}^{\prime }$ is unstable or superstable non-classifiable, then the isomorphism of models of $\mathcal{T}$ is continuous reducible to the isomorphism of models of ${\mathcal{T}}^{\prime }$.