Talk held by Thilo Weinert (KGRC) at the KGRC seminar on 2018-11-08.
Abstract: The history of the polarised partition relation goes back to the original seminal paper by Erdős and Rado from 1956. For the ordinary partition relation after some time one also investigated order-types. For the polarised partition relation however, I am only aware of three papers where order-type played a role and here nothing beyond well-orders ever seems to have been considered.
We are attempting to rectify this. We will present an analogue of a theorem of Jones and a potentially vacuous generalisation of a proposition of Garti and Shelah. Furthermore we will show limits to further generalisations and analogues and will exhibit some open problems.
This is joint work with Lukas Daniel Klausner.