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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sat, 8 Feb 2025 22:54:46 +0100
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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