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 $κ^κ$ for an uncountable $κ$ with the property $κ^{<κ}=κ$. The theory looks quite different from its classical counterpart where $κ=ω$, although some basic theorems do generalise.

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