First order logic, set theory and God

[Reltzik]

A composite phenomenon, based on the principle of limitation, cannot be a self-caused phenomenon. That is one thing we should keep in mind.

Yes, but I am questioning the principle of self-limitation's validity as an axiom.

As for the rest of your post, perhaps it must be clarified that Hatcher's proof was meant to provide a cut-and-dried deduction of the existence of a minimal concept (ie. a "universal uncaused cause") from a set of self-evident and empirically grounded axioms. While the proof doesn't tackle the fuller characterizations of God, there is at least little logical doubt that something akin to this minimalist understanding of a "God" is entirely believable and plausible as a distinct entity that has an existence, though perhaps little relation to what religious folks these days think of as a personal God.

Yes, but why call it god? It's so divorced from both the common conception and most philosophical conceptions that the choice of term can only engender confusion. This is an equivocation land mine just waiting for someone to trigger it.

To field one more objection to the proof, it does not handle a scenario of cyclical time, perhaps from Big Bang/Crunch cycles. Here you can have A causing B which turns around to cause A, with a sequence of causes regressing into the (repeated) past ad infinitum.