Can you imagine if set theorists were like type theorists and came up with a New and Improved set theory every few years? Like imagine being a mathematician and you want to formalize your material and you find yourself having to shop around for set theories, listening to people say oh ZFC that old thing? We don't use that anymore, we use this new and improved set theory with extra axioms, it's got classes and universes and whatnot
It's a miracle that a vast majority of working mathematicians settled on ZFC because it's like as if computer scientists looked at the very original calculus of constructions (no universe hierarchy, only lambdas) with definitions (for the programmers in the crowd) and simple inductive types (no mutual or nested, no parameters, nothing fancy) and went "yup, that's good enough! let's pack it up" and just settled with it
@ionathanch Didn't the vast majority of working mathematicians settle on naive set theory?
@ifazk I feel like that's what they'll use for everyday math, and then if they have need of anything specifically set-theory-ish they'll use ZF(C) since it's so established
That's the way it's been in math classes it seems, anyway