  By Easton's theorem one can force the exponential function on regular
cardinals to take rather arbitrary cardinal values provided monotonicity and
Koenig's lemma are respected. In models without choice we employ a "surjective"
version of the exponential function. We then prove a choiceless Easton's
theorem: one can force the surjective exponential function on all infinite
cardinals to take arbitrary cardinal values, provided monotonicity and Cantor's
theorem are satisfied, irrespective of cofinalities.
