Borel reductions and cub games in generalised descriptive set theory

Abstract

It is shown that the power set of $\kappa$ ordered by the subset relation modulo various versions of the non-stationary ideal can be embedded into the partial order of Borel equivalence relations on $2^\kappa$ under Borel reducibility. Here $\kappa$ is an uncountable regular cardinal with $\kappa^{<\kappa}=\kappa$.