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Borel orderings
We show that any Borel linear order can be embedded in an order preserving way into <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2 Superscript alpha"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>α<!-- α --></mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{2^\alpha }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for some countable ordinal <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha"> <mml:semantics> <mml:mi>α<!-- …