After Kurt Godel and his incompleteness theorem, mathematicians realized axioms can be pretty much whatever you want them to be. Making math, in my opinion, almost as much an art as a science. Here’s the time to get creative and introduce something radical (or not so radical).
Note: This is not a page to leave axiomatic systems unused. If that’s all you got, that’s all you got, but hopefully someone at least will come alongside and develop theorems and new math for all these new axiomatic systems that we will be defining in this space.
So feel free to come here and steal.