Colouring orders and ordering trees

One of the main motivations of generalised descriptive set theory is to use the Borel reducibility to study the complexity of theories. Following that motivation, one of the main question is whether the isomorphism relation of any classifiable theory is Borel reducible to the isomorphism relation of any non-classifiable theory. This has been proved to be consistent and under certain cardinality assumptions, the isomorphism relation of any classifiable theory is Borel reducible to the isomorphism relation of any stable unsuperstable theory.
In this talk we will study the isomorphism relation of unstable theories by merging Shelah's ordered trees method to construct models of unsuperstable theories and Hyttinen-Kulikov's coloured tree to construct Borel reductions.