[FOM] Question about Sigma-n classes in ZFC
owen@math.wisc.edu
owen at math.wisc.edu
Fri Aug 17 16:54:37 EDT 2007
To the set-theorists in particular, but the assembled experts in
general: are there any canonical properly Sigma-n classes -- i.e.
Sigma-n but not Sigma-m for any m < n -- for any n bigger than, say, n
= 1? I'm thinking of analogues to Tot, Inf or Rec in computability
theory, and I can't seem to find any in the the literature. In
particular, I'm looking for "natural" Sigma-n predicates that don't
have a "nice" analogue in Pi-n, whatever that might mean. Classes
definable over stronger systems than ZFC would be fine too, though I'd
prefer vanilla ZFC if possible.
Thanks for your consideration,
Robert Owen
owen at math.wisc.edu
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