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FORCING AXIOMS AND THE CONTINUUM HYPOTHESIS,PART II:TRANSCENDING ω1-SEQUENCES OF REAL NUMBERS
FORCING AXIOMS CONTINUUM HYPOTHESIS TRANSCENDING ω1-SEQUENCES OF REAL NUMBERS
2015/8/17
The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the Continuum Hypothesis. This answers a longstanding problem of Shelah.
One way to formulate the Baire Category Theorem is that no compact space can be covered by countably many nowhere dense sets. Soon after Cohen’s discovery of forcing, it was realized that it was natur...