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Apr 13, 2018 at 18:04 comment added Asaf Karagila @IianSmythe: Just consider the case where $c_0=c\times r$ and $c_1=c\times s$, where $r$ and $s$ are mutually generic over $M[c]$.
Apr 13, 2018 at 17:14 vote accept Jonathan Schilhan
Apr 13, 2018 at 17:04 comment added Jonathan Schilhan @IianSmythe Yes this is definitely possible. Their intersection could be some intermediate common Cohen extension.
Apr 13, 2018 at 15:31 answer added Gabe Goldberg timeline score: 13
Apr 13, 2018 at 15:11 comment added Iian Smythe Do you know if it's possible for (the reals of) $M[c_0]\cap M[c_1]$ to be something other than (the reals of) $M$, $M[c_0]$, or $M[c_1]$, in the Cohen case?
Apr 13, 2018 at 14:54 history edited Jonathan Schilhan CC BY-SA 3.0
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Apr 13, 2018 at 13:38 history asked Jonathan Schilhan CC BY-SA 3.0