Re: The set of necessary FISONs

On 31.01.2025 15:46, Richard Damon wrote:

On 1/31/25 5:21 AM, WM wrote:

 From this set O every finite subset can be subtracted without changing the result. Therefore,  by induction, no finite A(n) remains. Therefore the set O has no first ordinal. Therefore it is not a set of ordinals. Therefore your claim is wrong.

Induction doesn't work that way.

It works that way: When n belongs to ℕ, then n+1 belongs to ℕ.
And it works also thos way:
When n can be deleted, then n+1 can be deleted. Nothing remains.

There is no requirement that a "minimal" set exists.

There is the assumption that a set with U(A(n)) = ℕ exists. No element remains. The set does not exist.
Regards, WM