About set theory with urelements and elementary particles

Platonists seek a reality in mathematics, associated with the
truth of axioms.
Logicists and formalists are concerned about consistency and
independence of axioms but not about their truth.
I suggest, as a Platonist, that the axioms definitely true
are those applied to previously unsolved mathematical problems
or to physics or social sciences or ethics.

For the case of the axiom of choice, I state that the negation
of the axiom of choice is true because I apply it to quantum
mechanics and cosmology which are part of physics.
It is because of the lack of interdisciplinary research that
the status of the axiom of choice remains ambiguous.
People do not think unity of knowledge a good thing.

In XiUi with Ui a set of locations, i does not have to be
a count of time. We consider simple sequences of locations.

Let S be a finite well ordered subset of U, we can define
a distance by counting the number of urelements(non sets)
between two urelements.
Mr Andreas Blass corrected with number of urelements between
two urelements +1.
This applies for space and time as well.

Mr Andreas Blass pointed out the lack of useful coordinates and
that there is no vector space because it would be non denumerable.

My idea might insert itself where a reality is out of reach
of the usual model.
Then, there is the embedding theorem of Sochor and Jech of
U in V.
Mr Andeas Blass pointed out that the embedding is complicated,
involving sets of sets of ordinals.

As time as U is not well ordered, except in S above, there are
less causality relationships at the level of elementary particles
than at our level because causality is based on time ordered.
Adib Ben Jebara
http://jebara.topcities.com

Urelements, which are just elements of sets in non-standard set theory that do not obey the set axioms, don't seem to add much to set theory. When you add urelements to set theory, you mostly learn about urelements.

For a set, ¬ (A in A) is obeyed, while an urelement can have B = { B }, or
C = { { { { ... { C } ... }, 3}, 2}, 1}. But all of this magic is just accomplished by overloading the meaning of { }, and the "in" operator. If you give {, } , and the "in" operator just one meaning, you can define objects that work like urelements with respect to different operators.

If you are concerned with the Truth of the utility of urelements, then you should not be concerned with Plato the philosopher, but Bacon and Newton, which is to say, science. What good is an urelement? What can best be modelled by it?

Thank you for your posting.
With urelements, there is a difference in the axiom of choice.
Adib Ben Jebara.