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Nov 19, 2010 at 7:25 history edited Bjørn Kjos-Hanssen CC BY-SA 2.5
added assumption of Projective Determinacy
Nov 19, 2010 at 5:45 comment added Andrés E. Caicedo As a remark, this example is not strictly what I am hoping for, since the $\Delta^1_{2n+1}$-jump is not definable in a Borel way. (There are other examples of the phenomenon I'm looking for if we allow large cardinals, so I'm specifically looking for a Borel set, see for example this answer: mathoverflow.net/questions/45257/when-can-we-detect-forcing/…) Anyway, Kechris's result certainly gives a very natural projective example that definitely involves set theory under PD, I'll have to think about it.
Nov 18, 2010 at 18:16 comment added Andrés E. Caicedo Hi Bjørn, thanks for this new example! I'll try to find Kastanas paper.
Nov 18, 2010 at 17:59 history edited Bjørn Kjos-Hanssen CC BY-SA 2.5
changed the example
Nov 18, 2010 at 11:17 history answered Bjørn Kjos-Hanssen CC BY-SA 2.5