It's what you have to base everything else on. It comes prior to everything else. Free Will is on the same level as the Cogito. Everything else comes after.
I think, therefore I am. What is part of identity? Free will. If not free will, then there is no identity, no "I".
Axiomatic means unquestionable. The meaning of axiom as a premise for an argument came later.
Not really; I challenge you to find a dictionary that says the two terms are synonymous.
Originally an axiom was a proposition that was "self-evident". But there's a long history of people questioning "self-evident" propositions, happily for us.
There seems to be a colloquial usage of "axiom" to mean a proposition that someone doesn't want us to question. I deprecate that usage. For example, the Law of The Excluded Middle is an axiom, but it has often been questioned; ergo, it is not unquestionable.
And you've devolved here into semantics. The point is that for you to even think about the subject, you must have free will. If you are not deciding to think about it, then you are not thinking about it.
I think, therefore I am. What is part of identity? Free will. If not free will, then there is no identity, no "I".
Axiomatic means unquestionable. The meaning of axiom as a premise for an argument came later.