When a partial Borel order is linearizable

Abstract

We prove the following classification theorem of the ``Glimm -- Effros'' type for Borel order relations: a Borel partial order on the reals either is Borel linearizable or includes a copy of a certain Borel partial order $\meo$ which is not Borel linearizable.

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• Linearization of analytic order relations
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• On countable cofinality of definable chains in Borel partial orders
• Linearization of partial quasi-orderings in the Solovay model revisited
• Bounding and decomposing thin analytic partial orderings