Re: The set of necessary FISONs

On 10.03.2025 23:07, Jim Burns wrote:

I thought you (WM) might be interested to hear that
we can prove that proofs.by.induction are reliable
for FISONs.
 

That is trivial. I am interested in the difference you see between
Zermelo's Z₀ defined or ensurede by induction:
{ } ∈ Z₀,
and if
{{{...{{{ }}}...}}} with n curly brackets ∈ Z₀
then {{{...{{{ }}}...}}} with n+1 curly brackets ∈ Z₀.
and
the the set F of removable FISONs defined or ensured 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.
Regards, WM