Remarks on $\mathcal P_{\kappa}\lambda$-combinatorics
Tom 145 / 1994
Fundamenta Mathematicae 145 (1994), 141-151
DOI: 10.4064/fm_1994_145_2_1_141_151
Streszczenie
We prove that $\{x \in \mathcal P_\kappa \lambda\mid x \cap \kappa$ is almost $x$-ineffable$\}$ has $p_*({\rm NIn}_{\kappa, \lambda^{<\kappa}})$-measure 1 and $\{x \in\mathcal P_\kappa\lambda\mid x \cap \kappa$ is $x$-ineffable$\}$ has I-measure 1, where $\mathcal I$ is the complete ineffable ideal on $\mathcal P_\kappa\lambda$. As corollaries, we show that $\lambda$-ineffability does not imply complete $\lambda$-ineffability and that almost $\lambda$-ineffability does not imply $\lambda$-ineffability.
