First order logic, set theory and God

[YahwehIsTheWay]

With that being said, I would be more than curious to see if anyone could spot a noticeable error in Hatcher's logical deduction

Meh. Apologetics is for those of weak faith. I say "it's true because I know it's true." 

Logic and facts are for atheists. When you play the apologetics game, you play in their fields and that's where they've got you. They'll call for "evidence" and then say "extraordinary claims require extraordinary evidence" and that the "burden of proof" lies with you. 

They'll point out that logical arguments, even if they are sound, are not evidence. They are just arguments. At best, they constitute a weak standard of "proof" and so they are not "extraordinary" and thus you fall short of meeting your burden of proof. 

That's what they would say. 

Stick with faith.