Be careful with your phrasing there. The axioms for the real numbers [1] are complete and consistent (within ZFC). Hence I'm almost sure the axioms for each of

Be careful with your phrasing there. The axioms for the real numbers [1] are complete and consistent (within ZFC). Hence I'm almost sure the axioms for each of the finite dimensional vector spaces will also be complete and consistent. Part of the reason is that you can't define the integers within the context of the real numbers. [1]: https://math.stackexchange.com/questions/362837/are-real-numbers-axioms-a-consistent-or-complete-system https://math.stackexchange.com/questions/362837/are-real-num...