Towers on Trees
نویسندگان
چکیده
We show that (under MA) for any c many dense sets in Laver forcing L there exists a ff-centered Q Ç L such that all the given dense sets are dense in Q . In particular, MA implies that L satisfies MA and does not collapse the continuum and the additivity of the Laver ideal is the continuum. The same is true for Miller forcing and for Mathias forcing. In the case of Miller forcing this involves the correction of the wrong proof of Judah, Miller, and Shelah, Sacks, Laver forcing, and Martin's Axiom, Arch. Math. Logic 31 (1992), Theorem 4.1, p. 157.
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