typeswitch on Nostr: Now the standard natural numbers N in V give us the class 'N in *V, which contains ...

Now the standard natural numbers N in V give us the class 'N in *V, which contains every standard natural number '0, '1, '2, ... but also contains the class of any sequence of natural numbers, e.g. [(0, 1, 2, 3, ...)], and that's where we get nonstandard natural numbers from.

However. This 'N is actually the initial model of PA in *V, because one property of *V is that it also satisfies every first order property (expressible in the language of set theory) of V.

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