Yorioka [J. Symbolic Logic 67(4):1373-1384, 2002] introduced a class of ideals (parametrized by reals) on the Cantor space to prove that the relation between the size of the continuum and the cofinality of the strong measure zero ideal on the real line cannot be decided in ZFC. We construct a matrix iteration of ccc posets to force that, for many ideals in that class, their associated cardinal invariants (i.e. additivity, covering, uniformity and cofinality) are pairwise different. In addition, we show that, consistently, the additivity and cofinality of Yorioka ideals does not coincide with the additivity and cofinality (respectively) of the ideal of Lebesgue measure zero subsets of the real line.

中文翻译：

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论赖冈理想的基本特征

赖冈 [J. Symbolic Logic 67(4):1373-1384, 2002] 在康托空间上引入了一类理想（由实数参数化），以证明连续统的大小与实数上强测度零理想的共尾性之间的关系在 ZFC 中无法确定线路。我们构造了一个 ccc 偏序集的矩阵迭代来强制，对于该类中的许多理想，它们相关的基数不变量（即可加性、覆盖、均匀性和共尾性）成对不同。此外，我们始终表明，Yorioka 理想的可加性和共尾性与实线的 Lebesgue 测度零子集的理想的可加性和共尾性（分别）不一致。