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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Mon, 03 Mar 2025 12:01:59 -0500
Organization: Peripheral Visions
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WM formulated the question :
> On 03.03.2025 12:58, joes wrote:
>> Am Mon, 03 Mar 2025 09:48:16 +0100 schrieb WM:
>
>>>> Ah no, you're shifting the quantifier there.
>>> That is allowed if Zermelo can do it.
>> He can't.
>
> But it has been accepted that with all defined elements the set is defined.
>>> By induction Zermelo produces the set. Quantifier shift, obviously
>>> allowed by Zermelo. There is no other way to construct an infinite set.
>> A quantifier shift is never a valid deduction (even though the resultant
>> sentence may be true otherwise).
>
> Zermelo has no other deduction. The set is constructed by its elements.
>> 
>>>> The set of sets of FISONs that can be removed together does not contain
>>>> the set of all FISONs (although it does contain the infinite sets of
>>>> the odd or even FISONs).
>>> In exactly the same way as Z₀ is constructed by its elements, the set of
>>> removable FISONs is constructed by its elements.
>> And in the same way Z_0 doesn't contain the set of all elements.
>
> Of course not. It is the set of all elements.

Discrete elements.