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Dec 12 at 17:51 comment added Hanul Jeon @none I don't think your guess is true. If my question holds, then Goodstein's theorem implies the consistency of $\mathsf{PA+Con(PA)}$. I think there is a more direct proof, but I have no idea how to prove it.
Dec 12 at 10:02 comment added none I thought PA+CON(PA) proves Goodstein's theorem. So PA is just barely not strong enough.
Dec 10 at 18:20 history asked Hanul Jeon CC BY-SA 4.0