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 2ω.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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Spinas, O., Thiele, S. Additivity of the two-dimensional Miller ideal. Arch. Math. Logic 49, 617–658 (2010). https://doi.org/10.1007/s00153-010-0190-y
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DOI: https://doi.org/10.1007/s00153-010-0190-y