About set theory with urelements and elementary particles

Adib · March 6, 2008

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

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