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Aug 14, 2011 at 1:10 comment added Adam Bjorndahl Thank you! These are exactly the kind of helpful suggestions I was hoping for. I have convinced myself $F \cup G$ generates a unique ultrafilter just in case the condition you describe involving partitions of $\omega$ holds. I will update once I have carefully run the argument you suggested, to construct a positive answer to Q1 under CH. Again, the suggestion is much appreciated.
Aug 13, 2011 at 21:41 history edited Andreas Blass CC BY-SA 3.0
retracted over-optimistic idea
Aug 13, 2011 at 21:13 history answered Andreas Blass CC BY-SA 3.0