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Feb 7, 2021 at 17:20 history edited Patrick Lutz CC BY-SA 4.0
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Feb 7, 2021 at 17:03 comment added Patrick Lutz Yeah, I think this example is reasonably well-known (and I did not come up with it myself, to be clear). One interesting point is that the proof I give above actually shows that locally countable Borel partial orders can be Borel embedded into the "hereditarily a column of" partial order. The one use of choice can be done in the Borel context by the Lusin-Novikov theorem.
Feb 7, 2021 at 10:26 vote accept Ashutosh
Feb 7, 2021 at 10:26 comment added Ashutosh Thanks. This example also appears here (page 175): ams.org/books/conm/257/4033/conm257-4033.pdf
Feb 7, 2021 at 8:15 history answered Patrick Lutz CC BY-SA 4.0