A class of counter-examples to the hypersection problem based on forcing   equations
  We give a class of three-dimensional Stein spaces W together with a hypersurface H, such that the complement W-H is not Stein, but such that for every analytic surface S \subset W the complement S-S \cap H is Stein. This class is constructed using forcing equations and gives new counter-examples to the hypersection problem. 
Holger Brenner