Excellent course in set theory. Now I understand better the theory. I have a few questions, if I may.
My approach uses logic and the rules of non contradiction as my primary law. This lead me beyond the perceptual reality into metaphysics, which is everything that is real, everything else is experience, a relation between observer and substance. This relation only exists for and because of the observer.
I have a similar reduction to time, but it is in the form of substance and cause, the latter being built into the former. Essentially a monism where different variation of the same nature can undergo spontaneous logical operations. "Spontaneity" is the real attribute of time and it appears everywhere in this self evolving universe.
1) This reduction places us both in a pre-geometry situation. But is set theory also in a pre-logic situation? Can the rule of non contradiction originate in set theory, or is it the reverse?
2) Your schematics of electrons and hydrogen atom and nucleus appear to be very accurate. But what about the all pervasive time background?
3) I equate gravity with a higher probability of existence where time passes at a slower pace, which accounts for its universal application to everything and anything that exists. How does set theory surrender gravity and does set theory allow gradients in the rate of the time background for such a probability of existence. My approach has a single and unique type logical cause that is: existence is more probable where time runs slower. Would that be your time precursor arrow?
4) I presented a creation of the universe from nothingness where the only substance allowed is time because it avoids the contradiction between existence and non existence. In that, I take the rule of non contradiction as the ultimate rule of pre everything. It is the only rule that protects both the identity and existence of everything. What role does the rule of non-contradiction play in set theory?
I have two previous FQXI essays on the subject. At any rate, the set theory seems to offer a causal structure for the explosive evolution of time, all forking away from the origin, never going back... this is the arrow of time.
I thank you for that.