This is an announcement for the paper "A weak* separable C(K)* space whose unit ball is not weak* separable" by Antonio Aviles, Grzegorz Plebanek and Jose Rodriguez. Abstract: We provide a ZFC example of a compact space K such that C(K)* is w*-separable but its closed unit ball is not w*-separable. All previous examples of such kind had been constructed under CH. We also discuss the measurability of the supremum norm on that C(K) equipped with its weak Baire sigma-algebra. Archive classification: math.FA math.GN Submitted from: avileslo@um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1112.5710 or http://arXiv.org/abs/1112.5710