Re: The set of necessary FISONs

On 11.02.2025 21:01, joes wrote:

Am Tue, 11 Feb 2025 10:31:48 +0100 schrieb WM:

The set F of FISONs which can be removed without changing the assumed
result UF = ℕ is the infinite set F of all FISONs. This is proven by
just the same induction as Zermelo proves his infinite set Z.

Nope, any *finite* set of FISONs can be removed. The set of *those*
is infinite, but no set of removable FISONs is.
(Zermelo or whoever don’t prove the membership of infinite elements.)

Zermelo proves the existence of the set Z which contains the infinite set ℕ of all finite natural numbers.
I prove the existence of the infinite set F of all finite FISONs removable without changing the result of UF.
Note: Inductive sets are infinite.
Regards, WM