[FOM] Sigma-n classes in ZFC once again

owen@math.wisc.edu owen at math.wisc.edu
Mon Aug 20 13:56:52 EDT 2007

My earlier request missed something rather important: are there any  
canonical properly Sigma-n classes *other* than the usual universal  
Sigma-n class, or easy tweaks thereof?  [The latter being the obvious,  
and indeed usually only, example.]  That was the point of looking for  
something like Rec; it's a set with a natural description that is not,  
a priori, equivalent to "the universal Sigma-3 set".  In fact, I'd  
like to go further and ask if there are any standard "Post-like"  
proper Sigma-n classes -- that is, properly Sigma-n classes that are  
not equivalent (modulo some natural notion of equivalence) to the  
universal Sigma-n class -- in the literature.

[As you can see by my vagueness, this isn't something I've been able  
to formalize so even help in that regard would be greatly appreciated.]

Thanks for your time,

Robert Owen
owen at math.wisc.edu

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