  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.

Logic