[FOM] Omega Consistency of Q Implies Consistency of PA?

Joseph Shipman JoeShipman at aol.com
Wed Apr 15 14:59:42 EDT 2015

If "If epsilon-zero is well-ordered then PA is consistent" can be proven in Q then this follows immediately, because Q can go from "PA is inconsistent" to "there exists n such that the Goodstein sequence starting with n fails to terminate" while also proving termination (very lengthily!) for each specific n.

-- JS

Sent from my iPhone

> On Apr 15, 2015, at 10:49 AM, Richard Heck <richard_heck at brown.edu> wrote:
> Feferman mentions in a footnote in "Arithmetization" that Kreisel showed that the omega consistency of Q finitistically implies the consistency of PA. Unfortunately, the paper to which he refers seems to be hard to get. Can anyone explain the proof of this?
> Richard Heck
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