[FOM] Church-Kleene or Feferman-Schutte

[Thilo]

As fas as I remember all the proof-theoretic ordinals are recursive since they correspond to the strength of some recursive axiom system. So \Gamma_0 would be much smaller than \omega_1^CK.

But I am no proof-theorist so it would be better if someone feeling more confident about this could confirm it.

Regards,
Thilo Weinert


Am 14.05.2013 um 01:03 schrieb Sandro Skansi:

> I was looking through my books and journals for to compile a list of ordinals used in proof theory, but I did not seem to find anything that could really help me make a diagram, except for Pohlers 1996 BSL article. There I found almost everything, but I was not able to find this, so I am asking it here on the FOM list:
> 
> In terms of ordinals, starting from \omega, which one comes first, the Church-Kleene ordinal (\omega_1^CK) or the Feferman-Schutte ordinal (\Gamma_0)?
> 
> Best regards,
> 
> Sandro Skansi
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