On Borel Reducibility in Generalised Baire Space
  In this paper we study the Borel reducibility of Borel equivalence relations, including some orbit equivalence relations, on the generalised Baire space $\kappa^\kappa$ for an uncountable $\kappa$ with the property $\kappa^{<\kappa}=\kappa$. The theory looks quite different from its classical counterpart where $\kappa=\omega$, although some basic theorems do generalise. 
Sy-David Friedman, Tapani Hyttinen, Vadim Kulikov
math.LO