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Jul 20, 2018 at 17:39 vote accept Iian Smythe
Jul 20, 2018 at 14:11 comment added Miha Habič @WillBrian That is a good point! I didn't realize that.
Jul 20, 2018 at 13:16 comment added Will Brian Let me point out that statement $1$ in your theorem follows from the Sacks property. So you can conclude, for example, that Silver forcing (which has the Sacks property) also has the OP's property.
Jul 20, 2018 at 13:01 history answered Miha Habič CC BY-SA 4.0