An Easton-like Theorem for Zermelo-Fraenkel Set Theory Without Choice (Preliminary Report)

Anne Fernengel, Peter Koepke

Published 2013-08-07Version 1

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.