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May 13, 2022 at 4:58 history edited Martin Sleziak CC BY-SA 4.0
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Jun 15, 2020 at 7:27 history edited CommunityBot
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Apr 13, 2017 at 12:58 history edited CommunityBot
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Apr 16, 2014 at 5:45 comment added Noah Schweber I'm still interested in the remaining questions, but this is certainly enough for now!
Apr 16, 2014 at 5:44 vote accept Noah Schweber
Mar 29, 2014 at 19:35 history edited Ali Enayat CC BY-SA 3.0
edited body
Mar 29, 2014 at 14:17 comment added Ali Enayat Noah, I revamped my argument since contrary to my initial claim, Harrington's theorem has a limitation on $M$ (which makes perfect sense in light of the considerations of projective absoluteness discussed in Joel's answer). At the moment I do not know if the countable structures can be arranged to be ordinals. I also do not know the answer to your "quick question".
Mar 29, 2014 at 14:13 history edited Ali Enayat CC BY-SA 3.0
added 1845 characters in body
Mar 29, 2014 at 8:37 comment added Noah Schweber This is a really beautiful argument. One quick question: in the resulting $M[G]$, can the two now-non-equivalent ordinals be made second-order equivalent once again? (Really, that should be "for some $M$ . . .")
Mar 28, 2014 at 18:39 comment added Noah Schweber This is really interesting - thank you very much!
Mar 28, 2014 at 10:27 history answered Ali Enayat CC BY-SA 3.0