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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Tue, 11 Mar 2025 09:03:55 +0100
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On 10.03.2025 22:04, Alan Mackenzie wrote:
> WM <wolfgang.mueckenheim@tha.de> wrote:
>> On 10.03.2025 20:37, Jim Burns wrote:
> 
>>> ⎝ Therefore, this a property with no exceptions.
>>> is reliable.
> 
>> Do you really expect that your gobbledegook is of interest???
> 
> I find it of interest, yes.  It refutes _your_ gobbledegook in a way that
> you cannot answer.

I can. Only this question is of interest:

Zermelo's Z₀ is defined by induction:
{ } ∈ Z₀,
and if
{{{...{{{ }}}...}}} with n curly brackets ∈ Z₀
then {{{...{{{ }}}...}}} with n+1 curly brackets ∈ Z₀.

Likewise the the set F of removable FISONs
F(n) = {1, 2, 3, ..., n}
is defined by induction.
ℕ \ F(1) = ℵo,
and if ℕ \ F(1) \ F(2) \ F(3) \ ... \ F(n) = ℵo
then ℕ \ F(1) \ F(2) \ F(3) \ ... \ F(n+1) = ℵo.

What is the difference in your opinion?
JB has claimed that UF = ℕ ==> Ø = ℕ is wrong.

Regards, WM