Re: The set of necessary FISONs

On 3/10/2025 1:20 PM, WM wrote:

On 10.03.2025 17:31, Jim Burns wrote:

On 3/10/2025 4:42 AM, WM wrote:

For example, here:
⎛ A  FISON is linearly ordered,
⎜ begins at 0, ends at a FISON.end,

>
That is sufficient.

The real interval [0,x] is linearly ordered,
begins at 0, and,
if [0,x] is a FISON, ends at a FISON.end.
A real interval isn't what you mean by 'FISON'
is it?
Or do I need to add 'FISON' to
my WM.to.language dictionary?
⎛ definableᵂᴹ  ==  finiteⁿᵒᵗᐧᵂᴹ  ==  #A<#Aᣕᵇ
⎜ darkᵂᴹ  ==  finiteⁿᵒᵗᐧᵂᴹ  ==  big and #A<#Aᣕᵇ
⎜ matheologicalᵂᴹ  ==  infiniteⁿᵒᵗᐧᵂᴹ  ==  #A=#Aᣕᵇ
⎝ ...
If real interval isn't what you mean,
then that is _insufficient_

And that is what I use, except 0.

You would be better served by using this:
⎛ A  FISON is linearly ordered,
⎜ begins at 0, ends at a FISON.end, and,
⎜ for each split,
⎜ its foresplit ends at i or is empty  and
⎜ its hindsplit begins at j or is empty,
⎝ i and j such that i+1 = j

Peano and Zermelo and Cantor and I
describe infinitely.many.

>
Yes, without end.

The descriptions end.
What is described is without end.
Not.first.false claims are true
about what does not end
because _the descriptions_ end (are finite).
Because _the claims_ are finitely.many,
if there is a false claim,
then there is a first.false claim.
If each claim is true.or.not.first.false,
then each claim is not false.