Re: The set of necessary FISONs

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