On Borel Reducibility in Generalised Baire Space

TL;DR

This paper explores the structure of Borel reducibility among equivalence relations on the generalized Baire space, revealing differences from the classical case when =7.

Contribution

It extends the theory of Borel reducibility to uncountable , highlighting new phenomena and generalizing some classical results.

Findings

Different behavior of Borel reducibility for uncountable 

Generalization of some classical theorems to ^

Analysis of orbit equivalence relations in the generalized setting

Abstract

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.