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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sat, 15 Feb 2025 15:52:06 +0100
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On 15.02.2025 14:13, FromTheRafters wrote:
> WM was thinking very hard :
Each FISON and all its predecessors are proven omissible by
>> induction. This implies that the whole set is omissible.
> 
> Only if there were such a thing as a last FISON being omitted.

You are clearly wrong! Induction concerns the whole set. Compare 
Zermelo: "In order to secure the existence of infinite sets, we need the 
following axiom." [Zermelo: Untersuchungen über die Grundlagen der 
Mengenlehre I, S. 266] This is the axiom of infinity proved by 
induction. It ascertains the existence of an infinite set. It ascertains 
the set Z, Z_0 and the union of singletons ℕ.

Regards, WM