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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sun, 9 Feb 2025 15:48:36 +0100
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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.

Regards, WM