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Jul 25, 2011 at 15:29 comment added Cole Leahy Indeed, I am doubly silly. Of course the R from the original question is hyperarithmetical; we've shown that there is a hyperarithmetical Q meeting my description, and Q and R are coextensive! Please cut me some slack here, as I'm just learning. And I haven't had coffee today.
Jul 25, 2011 at 15:10 comment added Cole Leahy That was silly of me! I corrected the original posting. Thanks for the tip.
Jul 25, 2011 at 14:59 comment added Ali Enayat @Cole: I am not sure what you mean by Borel here; all subsets of $\omega$ are Borel if Borel is interpreted in its usual way.
Jul 25, 2011 at 14:54 comment added Cole Leahy Does this mean that the set R from the original question is indeed hyperarithmetical, and not just Borel? It was obtained by stacking, after all.
Jul 25, 2011 at 12:06 history answered Andreas Blass CC BY-SA 3.0