Towers on trees
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- by Martin Goldstern, Mark J. Johnson and Otmar Spinas PDF
- Proc. Amer. Math. Soc. 122 (1994), 557-564 Request permission
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.References
- Haim Judah, Arnold W. Miller, and Saharon Shelah, Sacks forcing, Laver forcing, and Martin’s axiom, Arch. Math. Logic 31 (1992), no. 3, 145–161. MR 1147737, DOI 10.1007/BF01269943
- Richard Laver, On the consistency of Borel’s conjecture, Acta Math. 137 (1976), no. 3-4, 151–169. MR 422027, DOI 10.1007/BF02392416
- A. R. D. Mathias, Happy families, Ann. Math. Logic 12 (1977), no. 1, 59–111. MR 491197, DOI 10.1016/0003-4843(77)90006-7
- Arnold W. Miller, Rational perfect set forcing, Axiomatic set theory (Boulder, Colo., 1983) Contemp. Math., vol. 31, Amer. Math. Soc., Providence, RI, 1984, pp. 143–159. MR 763899, DOI 10.1090/conm/031/763899
- Boban Veli ković, CCC posets of perfect trees, Compositio Math. 79 (1991), no. 3, 279–294. MR 1121140
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 557-564
- MSC: Primary 03E50; Secondary 03E05, 06A07
- DOI: https://doi.org/10.1090/S0002-9939-1994-1284459-3
- MathSciNet review: 1284459