Additivity of the two-dimensional Miller ideal

Archive for Mathematical Logic 49 (6):617-658 (2010)
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Abstract

Let ${{\mathcal J}\,(\mathbb M^2)}$ denote the σ-ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of ${{\mathcal J}\,(\mathbb M^2)}$ is bigger than the covering number of the ideal of the meager subsets of ω ω. We also show that Martin’s Axiom implies that the additivity of ${{\mathcal J}\,(\mathbb M^2)}$ is 2 ω .Finally we prove that there are no analytic infinite maximal antichains in any finite product of ${\mathfrak{P}{(\omega)}/{\rm fin}}$

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References found in this work

Happy Families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Set Theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
Sacks Forcing, Laver Forcing, and Martin's Axiom.Haim Judah, Arnold W. Miller & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):145-161.
Generic Trees.Otmar Spinas - 1995 - Journal of Symbolic Logic 60 (3):705-726.

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