Timeline for Is there a relational countable ultra-homogeneous structure whose countable substructures do not have the amalgamation property?
Current License: CC BY-SA 3.0
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| Jul 30, 2011 at 15:05 | comment | added | Ali Enayat | @Itai: You are right, the book defines it as you say, but the proof of Theorem 2.3.1 does not use disjointness. Maybe stable structures behave very differently for this problem. | |
| Jul 30, 2011 at 9:20 | comment | added | Itaï BEN YAACOV | Thanks! A side remark - I took a look in the book, and they define "amalgamation" with stricter requirement (what some call disjoint amalgamation), making the result as stated weaker than what is needed. However, insomuch as I understood the proof, it also works for the usual model-theoretic notion of amalgamation. But this requires arithmetic! Can one prove that this is impossible for, say, a stable structure? | |
| Jul 30, 2011 at 9:16 | vote | accept | Itaï BEN YAACOV | ||
| Jul 29, 2011 at 19:08 | history | edited | Ali Enayat | CC BY-SA 3.0 |
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| Jul 29, 2011 at 18:59 | comment | added | Ali Enayat | @Emil, thanks for your comments; I now see that I did say that $X$ is any prescribed subset of $\omega$. I will fix that. | |
| Jul 29, 2011 at 18:00 | comment | added | Emil Jeřábek | This is a nice example. A couple of points: (1) does not hold in general if the model does not have quantifier elimination. (3): what is $X$ in the theorem? | |
| Jul 29, 2011 at 17:40 | history | answered | Ali Enayat | CC BY-SA 3.0 |