On 10/17/2022 02:42 PM, Ross A. Finlayson wrote:
> On Monday, October 17, 2022 at 1:36:36 PM UTC-7, Ben Bacarisse wrote:
>> Antonio Speltzu <spe...@gmail.com> writes:
>>
>>> How did Godel, so smart as he was, use such an absurd numbering
>>> system?
>> What's absurd about it? It's simple, easy to understand and makes
>> proving that all the key functions are primitive recursive trivial.
>> There's nothing absurd about a simple scheme that does the job required
>> of it.
>>
>> --
>> Ben.
>
>
> It's just that an arithmetization implies a correspondence between items and integers.
>
> It's as if he had a well-ordered universe of theorems.
>

Ah: an arithmetization implies a correspondence between items
and integers, and all of the arithmetic relations.

One way to look at natural numbering for arithmetizations,
is to implement set theory in an arithmetization,
then carry down from that set theory, then to build
arithmetic from that with regards to them being
same objects, about the square-free in arithmetic
for the natural modeling of sets their elements
where the inductive elements are primes, in this
kind of way helping to illustrate that an inductive
set by itself, is only the most tenuous sort of trepidation,
out over the ice.

That mathematics assumes that a cold waste-basket and
models a superhighway out over the trail over the
frozen lake, here is for rather directly showing
that there isn't a bridge to nowhere without a bridge.

Another way to look at Goedel numbering is that there
exists an integer continuum, and he just picks up and leaves off.

Goedel numbering of course is the key assignment of
"theorems", of arithmetic, to "elements" of arithmetic,
as what that it's a "theorization" in a model theory,
in model theory in model theory ..., of an "arithmetization".

So, it might help to relate Goedel's numbers,
of formulas, to formulas of numbers, about the
usual enough idea to result a geometrization,
the objects of all the spaces of geometry
embodying all the relations of arithmetic's numbers,
then for giving those numbers, that
it's of the ordinals insofar as they are,
of the cardinals, of the universe, of those.