Watching nice overview of Reverse Mathematics.
So far I learned:
a) Before Reverse Mathematics, there were the Constructivists who *hated* the Law of Excluded Middle and came up with the Axiom of Choice and a few other things that the presenter calls “Just too strong”.
b) After the Constructivists, came Reverse Mathematics and “all was well” and now he’s talking about Reverse Mathematics.
It seems that Reverse Mathematics doesn’t really mess around with Set Theory, sticking with regular things, trying to derive axioms from the theorems in the process.
It does so thanks to Turing / algorithms / computability. [that doesn’t mean you can actually do it on a computer – our computers aren’t powerful enough for a lot of things, but you can figure that it’s *possible* in theory].