Re: The set of necessary FISONs

On 28.02.2025 20:25, Jim Burns wrote:

On 2/28/2025 12:04 PM, WM wrote:

On 28.02.2025 16:52, Jim Burns wrote:

 

An inductive proof only proves about
a set which is its.owcn.only.inductive.subset,
like Z₀ and like ℕ, perhaps not like Z

>
Z contains many inductive subsets.

 (We don't know whether Z=Z₀ or Z≠Z₀)

Z contains every set a. Z_0 contains only 0, {0}, {{0}}, ...

 Consider this WM.inductive.proof:

It is sufficient for my purpose to consider
0, {0}, {{0}}, ... which is an infinite set produced by induction.
Regards, WM