Post #2264423
2026-05-07 13:31 UTC
@typeswitch@gamedev.lgbt @johncarlosbaez@mathstodon.xyz This I understand somewhat as the statement that "one cannot construct the standard (i.e. intended model of) N in *V but any model of PA in *V will have nonstandard elements."
Which to me would still be in line with the original quote. That is, to get the standard N one would have to adopt some meta theory (if that is even allowed?) but the standard (i.e. intended) N is definitely not a standard model of PA in *V in any meaningful way.
What am I missing?
Replies (1)
-
@typeswitch@gamedev.lgbt 2026-05-07 13:50
@papalex@mathstodon.xyz @johncarlosbaez@mathstodon.xyz I think the problem is confusing. There are three levels here: Peano Arithmetic (the theory), models of PA which live in ZFC set theory (the metatheory), and models of ZFC set theory which live in some ambient set/class theory (the meta-meta-theory). The "standard model of PA" is both a meta-theoretic idea that is internal to ZFC set theory (usually the initial model), and a meta-meta-theoretic idea that relates different models of set theory (N in V and its images).