论文标题
小型无限分区和无处居中的其他特征
Small infinite partitions and other features of the Nowhere Centered ideal
论文作者
论文摘要
引入了\ textIt {node nhere tother strone} $ \ mathcal {nc} $。这是$ω\timesΩ$的共同理想，其定义特征是$ x \ times y $的集合，其中$ x，y $是$ω$的无限子集，在商$ \ mathcal {p}（p}（ω\ timesω）（ω\ timesω）\ slash \ slash \ nathcal {nccal {nc nc} $中。该商具有可计数的分区，并且始终具有尺寸$ω_1$的分区，而$ \ Mathfrak {a}>ω_1$。这与其他明确的商形成了巨大的对比。提出了该理想的其他组合特征，以及一个具有相似，更高维度理想的家族的结果。
The \textit{nowhere dense ideal} $\mathcal{NC}$ is introduced. It is a coanalytic ideal of $ω\timesω$ whose defining characteristic is that the sets of the form $X\times Y$, where $X,Y$ are infinite subsets of $ω$, are dense in the quotient $\mathcal{P}(ω\timesω)\slash\mathcal{NC}$. This quotient has countable partitions and consistently has partitions of size $ω_1$ while $\mathfrak{a}>ω_1$. This represents a huge contrast with other definable quotients. Other combinatorial features of this ideal are presented, as well as some results on a family of similar, higher dimensional ideals.
