Re: The set of necessary FISONs

On 08.02.2025 18:43, Jim Burns wrote:

Do you use ω-1 ?

Not in this proof.:
The axiom of induction says: If any property or predicate P satifies
(P(1) /\ ∀k(P(k) ==> P(k+1)), then it describes all elements of an inductive = infinite set. That is satisfied by the set M of all FISONs which are useless in U(A(n)) = ℕ.
Therefore U(A(n)) = ℕ ==> U{ } = { } = ℕ. This is false. By contraposition we get ~{ } = ℕ ==> ~ U(A(n)) = ℕ.
Regards, WM