Let \preceq_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 \preceq_R has fairly high complexity with respect to Borel reducibility (e.g.\ if P is a Borel preorder then P \leq_B \preceq_R), although its exact classification remains open.

### Coloring linear orders with Rado's partial order

#### Abstract

Let \preceq_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 \preceq_R has fairly high complexity with respect to Borel reducibility (e.g.\ if P is a Borel preorder then P \leq_B \preceq_R), although its exact classification remains open.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/689915