Bounding by canonical functions, with CH
  We show that that a certain class of semi-proper iterations does not add omega-sequences. As a result, starting from suitable large cardinals one can obtain a model in which the Continuum Hypothesis holds and every function from omega_1 to omega_1 is bounded by a canonical function on a club, and so omega_1 is the omega_2-nd canonical function. 
Paul Larson and Saharon Shelah