[FOM] Question about Sigma-n classes in ZFC

[owen@math.wisc.edu]

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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