Re: The set of necessary FISONs

On 15.02.2025 14:40, Richard Damon wrote:

And since you build your claimed "set" by Naive Set theory, your sets are worthless.

Zermelo constructs his set in modern set theory. 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.

 The set you show is empty, is the set of FISONs that are individually not necessary.

The remaining set should have at least one element. But it has none.
Further it would be silly to claim that replacing a smaller FISON is helpful after a larger FISON has been removed.
Regards, WM