Re: The set of necessary FISONs

On 06.03.2025 12:08, Jim Burns wrote:

On 3/6/2025 3:54 AM, WM wrote:

Am 06.03.2025 um 02:52 schrieb Jim Burns:

 

I think that you (WM) are using a different dictionary.

>
I think that you (JB) should correct your statement:

 <<JB<WM>>>

>
You need not the intersection however because
Z₀ can also be defined by
{ } ∈ Z₀, and
if {{{...{{{ }}}...}}} with n curly brackets ∈ Z₀
then {{{...{{{ }}}...}}} with n+1 curly brackets ∈ Z₀.

>
No.

<</JB<WM>>>
 No BECAUSE
that doesn't DEFINE Z₀

It defines Z₀ precisely.

 What does your inductive description permit in Z₀
which should not be permitted in Z₀ ?
Anything.
Your description permits Bob, as long as
{Bob}, {{Bob}}, {{{Bob}}}, ... are also in Z₀

Induction excludes Bob. He is not in the empty set and not in the set containing the empty set and not in any set with more curly brackets.
Regards, WM