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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Towers on trees


Authors: Martin Goldstern, Mark J. Johnson and Otmar Spinas
Journal: Proc. Amer. Math. Soc. 122 (1994), 557-564
MSC: Primary 03E50; Secondary 03E05, 06A07
MathSciNet review: 1284459
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that (under MA) for any $ \mathfrak{c}$ many dense sets in Laver forcing $ \mathbb{L}$ there exists a $ \sigma $-centered $ Q \subseteq \mathbb{L}$ such that all the given dense sets are dense in Q. In particular, MA implies that $ \mathbb{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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1284459-3
PII: S 0002-9939(1994)1284459-3
Keywords: Laver forcing, Miller forcing, Martin's axiom, capturing density
Article copyright: © Copyright 1994 American Mathematical Society