First order logic, set theory and God

[Belacqua]

The Stanford Encyclopedia backs me up on this. What they say confirms what I have read elsewhere.

The only difference between Kalaam and Aquinas is the idea of "efficient cause".

They still both follow the same pattern 1) Everything that exists must have a creator, 2) There must have been a time before anything existed 3) Therefore there must have been a first creator, 4) That creator must not have it's own creator (breaks premise 1) 5) That creator was god.  QED

Now Aquinas' elaboration, as I said above is the assertion of "efficient cause" which has two parts 1) nothing can cause itself and 2) there must be a best way to create anything and that way must be the same for everything.  All it is doing is adding extra assertions onto an original argument in order that in the mind of Aquinas the argument cannot now be used to logic up a generic god, but to specifically demand the christian god is the only answer.

The problem is still that the premises are assumed and that a number of them are mutually exclusive, either god has to have a creator or it is not part of the set Everything, therefore non-existent.

I'm afraid your understanding of the whole thing is not very good. Both arguments do not state that "there must have been a time before anything existed." 

But you have the sources available, so I'll drop the subject.