[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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