Are Theists Illogical for Believing in God?

[Ramsin.Kh]

I really like that. Its an elegant argument, and easy for a non-specialist like myself to follow. Good stuff.

Thanks...

1. That any universe consists of a set of elements {1...n}.

Not necessarily, I've said any universe is a set of elements.

2. That every element either exists or doesn't exist. Either E(x) or not E(x).

If at least one element exists, then the universe exists. If no elements exist, then the universe does not exist.
The problem is of presupposing the axiom that every universe can either exist or does not exist.

I'm not sure what you've really meant in (1), but I can see that (2) is more important.
One aspect of realism is the dimension of existence. For something to be real it should exist.
The question is, Is a universe without any axioms real?
I'm also thinking of, Isn't 'the empty set of axioms indicating such emptiness' an axiom?
Is a universe possible without the axiom of causality?

No, they are mathematical descriptions of reality that use different axioms at their basis that make their mathematical formulation irreconcilable.

OK. They should share at least one mathematical axiom, for instance (a=a), since while writing a physics equation, one side of the equation must be dimensionally equal to its other side.

Then for everyone defining A as 'just logics' B would seem as adapted logic and C would seem illogic.
But for everyone defining C as 'just logics' A and B would seem illogic. So what is truth?

Therefore, in this respect, all universes are logical and illogical.