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Dec 30, 2014 at 0:02 history edited Joel David Hamkins CC BY-SA 3.0
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Dec 29, 2014 at 23:13 comment added Joel David Hamkins Gitman and Fuchs and I are currently preparing a paper on $\omega_1$-like models of set theory for which the embedding comparability theorems fail, and it is conceivable to me that one could build a multiverse using such models in which your joint embedding property fails.
Dec 29, 2014 at 23:06 comment added Kyle Gannon Thanks for your response. Might you know of a construction where these facts fail?
Dec 29, 2014 at 22:58 history answered Joel David Hamkins CC BY-SA 3.0