azul on Nostr: But if we stick to ZFC meta-theories, we still have the meta-meta-theoretic idea of a ...

But if we stick to ZFC meta-theories, we still have the meta-meta-theoretic idea of a "standard model of PA" as a model that exists across meta-theories, the image of N in V into this version of the meta-theory.

(If we don't do this, the question "is there a model of ZFC set theory where the standard model of PA is different from the initial model of PA" has the answer "no, by definition", which isn't very interesting.)