Re: The set of necessary FISONs

On 01.03.2025 18:47, Jim Burns wrote:

On 3/1/2025 7:51 AM, WM wrote:

Z_0 contains only 0, {0}, {{0}}, ...

 Z₀ = {0,{0},{{0}},...} is
the only subset of Z₀ which
holds 0 and, for each a, holds {a}

Z₀ is defined by induction.
Likewise UF is defined by induction.
ℕ \ F(1) \ F(2) \ F(3) \ ... = ℵo
= ℕ \ (F(1) U F(2) U F(3) U ...) = ℵo.

In narrower Z₀,
inductivity identifies a unique set.

So it is.
Regards, WM