[FOM] Goodstein's Theorem and Pi^1_1 comprehension

Aatu Koskensilta aatu.koskensilta at xortec.fi
Sun Apr 16 18:30:49 EDT 2006

On Apr 16, 2006, at 11:33 PM, William Tait wrote:

> Note that, although Steve Simpson points out in his book a close
> model-theoretic relation between PA and ACA_0, the latter system is
> proof-theoretically stronger: Its proof-theoretic ordinal is epsilon_
> {omega X 2}, I think---certainly it is at least epsilon_{omega}, as
> opposed to epsilon_0 for PA.

How can that be with ACA_0 (arithmetical comprehension + induction for 
sets) being conservative over PA? What am I missing?

Aatu Koskensilta (aatu.koskensilta at xortec.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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