05-27   Berichtsreihe des Mathematischen Seminars der Universität Kiel

## Additivity of the two-dimensional Miller ideal

Let \$\J(\miller^2)\$ denote the \$\s\$-ideal associated with two-dimensional Miller forcing. We show that it is relatively consistent with ZFC that the additivity of \$\J(\miller^2)\$ is bigger than the covering number of the ideal of the meager subsets of \$\baire\$. We also show that Martin's Axiom implies that the additivity of \$\J(\miller^2)\$ is \$2^{\o}\$. Finally we prove that there are no analytical infinite maximal antichains in any finite product of \$\pf\$.

Mathematics Subject Classification (1991): 03E15, 03E17, 03E50

Keywords: Miller forcing, Mathias forcing, forcing ideal, Cohen real