I wish to make a large digraph (network) linking various proofs together in mathematics from, say, the definition of a group to Galois theory. I got in my head that I wanted to do this after reading about the "truth mines" in Greg Egan's book, diaspora, which I would wholeheartedly recommend.
The issue is, at the moment I could only start this graph from naive set theory, starting with the "definition" of a set, of the natural numbers, and so on (though definition stretches things as I could not rigorously define a set as it stands). It seems like this potentially invites danger as there's a reason such set theory is called naive, it leads to paradoxes.
If I were to start this graph from naive set theory, could I then substitute in more advanced material later on and amend it, so for instance eventually linking the ZFC axioms to where I had previously started my graph? Or is naive set theory so far from the truth that I could not possible hope to untangle it?
I understand that this is a strange question, but don't you think it would be amazing to be able to see a map of the mathematical landscape?