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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Wed, 12 Feb 2025 07:08:10 -0500
Organization: Peripheral Visions
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WM wrote :
> On 12.02.2025 01:38, Jim Burns wrote:
>> On 2/11/2025 2:23 PM, WM wrote:
>>> On 11.02.2025 18:42, Jim Burns wrote:
>>>> On 2/11/2025 4:31 AM, WM wrote:
>> 
>>>>> The set F of FISONs which can be removed
>>>>> without changing the assumed result UF = ℕ
>>>>> is the infinite set F of all FISONs.
>>>>
>>>> Yes.
>>>
>>> Fine.
>>>
>>>>> This is proven by just the same induction
>>>>> as Zermelo proves his infinite set Z.
>>>>>
>>>>> Either you accept both proofs or none.
>> 
>> What is this "both proofs"?
>
> One is Zermelo's proof by induction that there is an infiite set Z.

It's an axiom, not a theorem.