We introduce a new method for building models of CH, together with \Pi_2 statements over H(\omega_2), by forcing over a model of CH. Unlike similar constructions in the literature, our construction adds new reals, but only \aleph_1-many of them. Using this approach, we prove that a very strong form of the negation of Club Guessing at \omega_1 known as Measuring is consistent together with CH, thereby answering a well-known question of Moore. The construction works over any model of ZFC + CH and can be described as a finite support forcing construction with finite systems of countable models with markers as side conditions and with strong symmetry constraints on both side conditions and working parts.
|Publication status||Submitted - 2017|