Re: The set of necessary FISONs

On 15.02.2025 14:13, FromTheRafters wrote:

WM was thinking very hard :

Each FISON and all its predecessors are proven omissible by

induction. This implies that the whole set is omissible.

 Only if there were such a thing as a last FISON being omitted.

You are clearly wrong! Induction concerns the whole set. Compare Zermelo: "In order to secure the existence of infinite sets, we need the following axiom." [Zermelo: Untersuchungen über die Grundlagen der Mengenlehre I, S. 266] This is the axiom of infinity proved by induction. It ascertains the existence of an infinite set. It ascertains the set Z, Z_0 and the union of singletons ℕ.
Regards, WM