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May 27 at 14:14 vote accept Zuhair Al-Johar
May 27 at 14:00 comment added Zuhair Al-Johar @TimothyChow, OK good suggestion. Thanks
May 27 at 13:39 comment added Timothy Chow @ZuhairAl-Johar If you have a materially different question from the one you originally posed, then the etiquette is that you create a new MO question, rather than edit your question, which can make it seem that the correct answers to your original question are wrong or misguided.
May 26 at 19:46 comment added Joel David Hamkins Ah, OK, in that case I've lost interest...
May 26 at 17:49 comment added Zuhair Al-Johar I've edited the question to meet the original intention that motivated it.
May 26 at 17:40 comment added Zuhair Al-Johar In reality the original question I had in mind was in relation to ZCA where I thought this incomparability can occur. Anyhow I think the underlying ZFA theory for FM permutation models have a replacement schema so the question might not be relevant to them. But anyhow. How can we prove matters in the setting of ZCA or even in ZFCA but with forbidding impure to pure replacement. I mean those I think can permit such incomparabilities, so how to settle such questions in these contexts. That's the essence of the question really.
May 26 at 17:34 vote accept Zuhair Al-Johar
May 26 at 17:49
May 26 at 14:05 history edited Joel David Hamkins CC BY-SA 4.0
added 16 characters in body
May 26 at 13:48 history answered Joel David Hamkins CC BY-SA 4.0