Borel orderings
Leo A. Harrington, David E. Marker, Saharon Shelah · Transactions of the American Mathematical Society · 1988
We show that any Borel linear order can be embedded in an order preserving way into 2 α {2^\alpha } for some countable ordinal α \alpha and that any thin Borel partial order can be written as a union of countably many Borel chains.