I'm not sure what you mean by this, particularly this phrasing: "sets of axioms where 1 = 1". 1 = 1 is an axiom, not something that's proven by any set of axioms.
But I'm willing to believe I'm simply naive here. You say there is some set of axioms which prove that 1 = 1. Are those axioms not agreements? Since you seem to be familiar, what are those axioms?
It is by definition. If you disagree, go write a mathematical proof that 1 = 1. There are many in the world who would love to see it.