Fodor space in generalized descriptive set theory

TL;DR

This paper explores the continuous reducibility of isomorphism relations in generalized descriptive set theory, particularly focusing on the space of functions over inaccessible cardinals and the complexity of model isomorphism relations.

Contribution

It establishes a connection between the reducibility of isomorphism relations for certain theories and their stability or non-classifiability in the context of generalized descriptive set theory.

Findings

Isomorphism of models of stable theories reduces to that of unstable theories.

For inaccessible ppa, certain theories' isomorphism relations are continuously reducible.

The work extends classical descriptive set theory concepts to higher cardinal frameworks.

Abstract

We study the continuous reducibility of isomorphism relations in the space of regresive functions in $\kappa^\kappa$. We show for inaccessible $\kappa$, that if $\mathcal{T}$ is a theory with less than $\kappa$ non-isomorphic models of size $\kappa$ and $\mathcal T'$ is unstable or superstable non-classifiable, then the isomorphism of models of $\mathcal{T}$ is continuous reducible to the isomorphism of models of $\mathcal{T}'$.