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Feb 22, 2015 at 19:23 comment added Asaf Karagila Mohammad, thanks for the reference! I've looked it up. It's a nice idea which sort of combines both mine and Joel's comments.
Feb 20, 2015 at 15:42 history edited Mohammad Golshani CC BY-SA 3.0
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Feb 20, 2015 at 15:33 vote accept Hanul Jeon
Feb 20, 2015 at 15:21 comment added Asaf Karagila @Joel: I would actually expect something slightly more clever than that. For example force over Cohen's first model in a way which doesn't add sets of ordinals, but encodes one of the generic reals into $\sf HOD$. But I'd much rather see the paper first.
Feb 20, 2015 at 15:18 comment added Asaf Karagila Do you have a reference for the paper?
Feb 20, 2015 at 14:11 history edited Mohammad Golshani CC BY-SA 3.0
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Feb 20, 2015 at 13:54 comment added Joel David Hamkins Could you say something about the proof? I imagine some kind of higher symmetric inner model of a model where $\text{HOD}^{\text{HOD}}\neq\text{HOD}$. For example, add a Cohen real, and then code it into the GCH pattern, but take a symmetric inner model of that model. So the idea is that the Cohen real will be in $\text{HOD}$, but not in $L_{SO}$.
Feb 20, 2015 at 13:14 history answered Mohammad Golshani CC BY-SA 3.0