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Sep 13, 2023 at 18:48 comment added Joel David Hamkins @Holo I posted another answer explaining this proof.
Sep 8, 2023 at 20:15 comment added Holo Great! I will be waiting for any updates
Sep 8, 2023 at 19:43 comment added Joel David Hamkins Yes, of course. I think there is a strategy outline now described in the comments on the main thread. I'm checking with some models-of-PA friends of mine about generalizing the PA result on isomorphic comp saturated models with same theory and same standard system to the additive case, and if that works, then we'll get the positive result.
Sep 8, 2023 at 19:07 comment added Holo Thanks for the answer, my intent in this question was the more general manner, indeed if we can show that given an additive cluster structure we can identify M up to isomorphism I would regard this as a positive answer
Sep 8, 2023 at 1:34 history edited Joel David Hamkins CC BY-SA 4.0
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Sep 7, 2023 at 23:52 history edited Joel David Hamkins CC BY-SA 4.0
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Sep 7, 2023 at 23:46 history edited Joel David Hamkins CC BY-SA 4.0
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Sep 7, 2023 at 23:36 history answered Joel David Hamkins CC BY-SA 4.0