Forcing axioms and the continuum hypothesis

David Aspero, Paul Larson, Justin Tatch Moore

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Woodin has demonstrated that, in the presence of large cardinals, there is a single model of ZFC which is maximal for ?-sentences over the structure (H(?), ?, NS), in the sense that its (H(?), ?, NS) satisfies every ?-sentence s for which (H(?), ?, NS) {true} s can be forced by set-forcing. In this paper we answer a question of Woodin by showing that there are two ?-sentences over the structure (H(?), ?, ?) which can each be forced to hold along with the continuum hypothesis, but whose conjunction implies,. In the process we establish that there are two preservation theorems for not introducing new real numbers by a countable support iterated forcing which cannot be subsumed into a single preservation theorem.
Original languageEnglish
Pages (from-to)1-29
Number of pages29
JournalActa Mathematica
Issue number1
Publication statusPublished - 1 Mar 2013


  • Continuum hypothesis
  • Iterated forcing
  • Forcing axiom
  • Martin's maximum
  • Π2 maximality
  • Proper forcing axiom
  • 03E35
  • 03E50
  • 03E57

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