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May 25, 2023 at 20:14 comment added Vladimir Kanovei I myself was informed a few days ago, see also DOI:10.1017/jsl.2017.75 for a JSL paper where the argument was reproduced.
May 24, 2023 at 19:28 history edited Hanul Jeon CC BY-SA 4.0
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May 24, 2023 at 19:26 comment added Hanul Jeon @VladimirKanovei I had not aware of Hamkins' argument, but it looks interesting.
May 24, 2023 at 5:40 comment added Vladimir Kanovei Yes it likely works, see also jdh.hamkins.org/diamond-on-the-ordinals with a similar argument, where the goal is an Ord-long Diamond yet the proof is adaptable to the $\omega_1$-long case.
May 22, 2023 at 22:22 history answered Hanul Jeon CC BY-SA 4.0