Few new reals

David Aspero, Miguel Angel Mota

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
JournalActa Mathematica
Publication statusSubmitted - 2017

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