Borel Reductions and Cub Games in Generalized Descriptive Set Theory

Abstract

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

21 pages. Generalized Descriptive Set Theory