Re: The set of necessary FISONs

On 2/17/2025 2:27 PM, WM wrote:

On 16.02.2025 19:39, Richard Damon wrote:

Just because there is not
individual FISON that when removed
changes the results,
doesn't mean that you can remove ALL.

>
Proofs by induction cover all FISONs.

Proofs by induction prove that
some property A(k) describes each element of
some inductive subset of
an inductive set with an only.inductive.subset.
There is only one set an inductive subset can be.
It is
the infinite inductive set with an only.inductive.subset.
We know,
because there's only one (infinite) set of elements
described by A(k),
that, for each of infinitely.many elements, it is A(k).
That reasoning is silent about
whether the _set_ (not its elements) has A(k).