On Borel equivalence relations in generalized Baire space (Q412067)

Let us consider the generalized Baire space \(\kappa^\kappa\) for an uncountable cardinal number \(\kappa\) such that \(\kappa^{<\kappa}=\kappa\). In the paper under review the authors focus on Borel reducibility of Borel equivalence relations on such a space. In particular, they construct two equivalence relations such that neither of them is Borel-reducible to the other (it is worth mentioning that the straightforward generalization of the corresponding example for \(\kappa=\omega\) does not work in this case). A small modification of the construction shows that the straightforward generalization of the Glimm-Effros dichotomy from \(\omega\) to \(\kappa\) fails.