Are Theists Illogical for Believing in God?

[Ramsin.Kh]

Here is an attempt, let's say that the set (N) is the collection of all the universes, whether logical or illogical.
N = {X, Y, Z, ...}
The elements (X), (Y) and (Z) are just existent real universes.

Notice that (N) does not necessarily exist in reality, in this case, it's an abstracted mental idea.
The elements of (N) do exist only if each of them contain something.
Every element/universe can be considered as smaller set, a subset, so:
X = {...}
Y = {...}

For a universe to exist, it should contain something. If a universe contains nothing then it's as good to say that such a universe does not exist, since even space and time have quantities and are something, therefore:
If: X = {A, B, ...} => This universe does exist.
If: Y = ∅ = {} => This universe does not exist and should be removed from (N) since (N) is a set for the existent universes.

For (X), its existence is an axiom, therefore it is logical and has no empty set of axioms.
For (Y), we know that it does not exist, it has an empty set of axioms, therefore no logical conclusions can be made of that.

Therefore: N ≠ ∅
All existent universes should at least share one axiom and that is the existence axiom:
(Axioms of Universe X) ∩ (Axioms of Universe Z) = [The axiom of existence]