ABSTRACT
In general this theorem can be improved by slightly sharpening the reduction to one that is provably or absolutely A these complexity classes are a little technical to define,17 but have the advantage of being just inside the region for which ZFC alone can prove regularity properties-such as any absolutely A function between Polish spaces is continuous on a comeager set. In this sharper form the theorem would then become a dichotomy theorem: (i) and a suitably amended version of (ii) would be incompatible.
