Coloring linear orders with Rado's partial order

摘要

Let R be the preorder of embeddability between countable linear orders colored with elements of Rado's partial order (a standard example of a wqo which is not a bqo). We show that R has fairly high complexity with respect to Borel reducibility (e.g. if P is a Borel preorder, then P B R), although its exact classification remains open.