“The notion of an 'actual infinity' is logically consistent/possible within Axiomatized Set Theory.”
But, so what? A concept's being logically possible (free of formal contradictions) doesn't entail that it is actually/metaphysically possible.1
Any interval contains an infinity of subintervals (e.g. a meter and minute can both be divided in half an infinity of times).12 This is relevant because if there are an infinity of sub-intervals inside any interval, then an actual infinity of subintervals must exist.
By way of response, however, intervals can only potentially infinitely be divided (i.e., divided, then divided again, then again, with no end), so it is not an actual (completed) infinity. That is to say, the interval it is not comprised of an infinity point-parts or divisions; instead, the interval is logically prior to any potential infinity of divisions/points that we continually impose on it by conceptually dividing it in half.
God is an infinite being. This is relevant because if God is an infinite being, then God's existence entails the existence of an actual infinity.
But wait, when we say God is infinite, we are ascribing a qualitative attribute to God (e.g. God is maximally good, powerful). We are not ascribing a quantitative infinity.
The extent of God's knowledge would be infinite (given God exists and is omniscient). So if actual infinities are impossible so is God.1
But so what if the extent is infinite? Couldn't it be that God's knowledge is metaphysically "simple", akin to a map, which isn't inherently propositional in form, but which can nevertheless be _represented _propositonally (e.g. city A is 3 miles from city B;one can get there via route xyz, etc.).2