Re: A question about FOL theories and models

["MoeBlee"]

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