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MoeBlee wrote:
> Rupert wrote:
> > If you're going to do model theory, you have to decide what metatheory
> > you're going to work in. You can prove that there exists a model of
> > Hilbert's axioms with the parallel postulate negated in fourth-order
> > Peano arithmetic, and any stronger theory, such as ZFC.
>
> What is the strength relation between Z (no schema of replacement) and
> n-order PA? Between ZF and n-order PA?
>
> Is Z equi-strong as 2nd order PA? Or is Z stronger than n-order PA, for
> all n?
>
> Thanks,
>
> MoeBlee
Z is stronger than n-order PA for all n. Z can prove that, for all n,
n-order PA is sound. ZF is much stronger still.
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