[Serious] Could an omnipotent and omniscient god prove that he was God?

[Objectivist]

How?  Arbitrary means unsupported by any evidence either perceptual or conceptual.  Once we are aware of some objects then a total is implicit.  An actual infinite can not exist.  It defies the law of identity.  By what means are you aware of these other existents that exist outside of the total and how can we distinguish these other existents from somehting that is merely imaginary?  It's these other existents that are arbitrary and we have a way of ruling them out.

Arbitrary, in the sense I'm using here, just means something like random. If it happens to be that the totality is just this one universe, with very specific initial constants that just are, then that's arbitrary to me. The constants could've been different values, there could've been more than one universe. So per my reasoning, this comes off as quite arbitrary.

Interesting statement you made about actual infinity. I don't see how it has to be impossible. Could you enlighten me on how, per Objectivism, the law of identity negates an actual infinite?

I'm not aware of anything that is beyond this universe, and nothing about my wording suggested that. I'm just using reason to see what could be possible, contemplating and asking questions based on my reasoning.

How have you ruled out those "arbitrary other existents" exactly?

Happy to learn more stuff about Objectivism from you, but I'm also here to share my perspective as well.

Yes, everything about your wording implies that there is something outside of the total of existence.  You said, "The total of what actually exists appears to be quite arbitrary if the total is basically this universe or a limited range of universes."  You are implying that I just picked some things to include in the total and left other things out.  I did not do this.  I defined the universe as everything that exists seen as a whole.  What did I leave out?  What rational justification is there for saying something exists but is not part of the total of what exists?  I'm very careful to define my terms objectively.  

How have I ruled out those "arbitrary other existents"?  By means of reason.  By recognizing that all concepts are open-ended.  They include a potentially infinite number of 
units.  The concept 'universe' which is synonymous with existence is the widest of all concepts.  There is nothing left out of it.  It includes all existents, their relationships, their identities, their actions, all their attributes...absolutely everything including things we aren't even aware of yet.  If I said that the universe was all matter, energy, space, and time, then that would be arbitrary.  That would be a reverse package deal and that would be a fallacy. Objectivism holds that they are objective.  They are the form in which we identify and retain knowledge of facts.  They carry our knowledge beyond the perceptual concretes of our surroundings to include the entirety of existence.