Why not? For the simple reason he can NOT be god in that case. That is mathematical. It is simply plainly impossible. God does not discriminate, otherwise he is NOT god.
And where did you get your degree in mathematics?
It seems you're operating with a pre-conceived notion of what God is or isn't, and marashalling arguments in order to "support" your notions. Here's a more sensible approach:
1. Either God is, or is not. If the latter, we're done; if the former, then:
2. Either God communicated with His critters (us), or He didn't. If the latter, we're done; if the former, then:
3. Either God made that communication widely available, or He didn't. If the latter, we're screwed; if the former, then:
4. Look to the major religions; they're the candidates. That leaves us with just a handful. Test them for internal consistency, historical "fit", reasonableness, and mystery -- any revelation of a real creator-God will have mystery.
So by basic good sense, your definition fails: any God who is God and communicates to His critters will be found (most likely) by examining one (or more!) of the major religions.
If He discriminates -- tough.
If it violates your notion of mathematics -- tough.
It may just be that the world is not what you believe it to be -- and that it should be is not surprising, in fact we should expect that part of God's revelation will explain some things about the world that aren't obvious. I know for certain that whatever mathematics you're thinking of is either fallacious in application or irrelevant, because I have a brother who was brilliant enough in math to have walked out on the accelerated doctoral program at Cal Berkeley because, essentially, it bored him -- and He says that the God of the Bible can be modeled mathematically quite easily.
So, where was your degree from, again?