Few new reals

David Asperó, Miguel Angel Mota (Lead Author)

Research output: Contribution to journalArticlepeer-review


We introduce a new method for building models of CH, together with Π2 statements over H(ω2), by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only ℵ1-many of them. Using this approach, we build a model in which a very strong form of the negation of Club Guessing at ω1 known as Measuring holds together with CH, thereby answering a well-known question of Moore. This construction can be described as a finite-support weak forcing iteration with side conditions consisting of suitable graphs of sets of models with markers. The CH-preservation is accomplished through the imposition of copying constraints on the information carried by the condition, as dictated by the edges in the graph.

Original languageEnglish
Article number2350009
Number of pages35
JournalJournal of Mathematical Logic (jml)
Issue number02
Early online date29 Jun 2023
Publication statusE-pub ahead of print - 29 Jun 2023


  • CH-preservasion
  • measuring
  • side conditions
  • adding reals
  • CH-preservation

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