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MATHEMATICAL LOGIC QUARTERLY
Volume -, Issue -, Pages -Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/malq.202300013
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We define a property of forcing notions and prove the existence of a model in which this property holds and the continuum hypothesis is negated, while the Cichon-Blass diagram of cardinal invariants matches that of the Cohen model. As a consequence, the forcing axiom and the forcing axiom for sigma-centered forcing notions are shown to be independent of each other.
We define a property of forcing notions and show that there exists a model of its forcing axiom and the negation of the continuum hypothesis in which the Cichon-Blass diagram of cardinal invariants is the same as in the Cohen model. As a corollary, its forcing axiom and the forcing axiom for sigma-centered forcing notions are independent of each other.
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