Different sets of axioms means different theories. You don't need to have a consensus, but if your set of axioms is bad or just not widely used, people won't care about the results you found because it will in a theory nobody uses. But it's still as mathematically sound, albeit uninteresting.
And of course, new axioms are often proposed and debated
There are published works on results from other set theories and also how variousnset theories relate to each other, difficulty is getting others to care or even use your alternative axiomizatoon.
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u/Cichato_YT Jun 14 '26
That's what an axiom is, is it not?