Re: The set of necessary FISONs

On 09.02.2025 13:34, joes wrote:

Am Sat, 08 Feb 2025 22:54:46 +0100 schrieb WM:

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.

Caveat: P is *not* satisfied by the set of all k, only by its elements.

Peano is not satisfied by the set of all k either. But no exceptioncan
be identified.