Oh yes, it's right up your alley. I can't claim to have gone deep into it, and it is extremely deep. I can't do the motivation justice on my phone, and I hate to recommend a book I JUST finished, but I'm going to.

I've studied the earlier stuff in set theory and logic a bit here and there over the years, and this book covers it all and then some, without the burdensome overhead of all the technicals that would make the subject take a year to study in school (or more). It's really a great balance with some philosophical angles added. I am certain you will learn from and enjoy it. I read it in 2 weeks of vacation on my downtime, and I read such things very slowly as a rule, so it's quite a fast read.

The beginning 20-30 pages is a bit slow, but just about everything after is gold. The end chapters in particular is where you get into a similar concept of large cardinals (defined by their properties rather than constructed).

From how to construct real numbers rigorously, godels completeness and incompleteness theorems, to non standard models of math, to additional axioms for consideration in set theory (existence of large cardinals creates this "infinitely nested" proof power; related to tree(3) proof sorta),... check out the table of contents and see for yourself.