We prove the consistency of: for suitable strongly inaccessible cardinal lambda the dominating number, i.e., the cofinality of ^{lambda}lambda, is strictly bigger than cov_lambda(meagre), i.e. the minimal number of nowhere dense subsets of ^{lambda}2 needed to cover it. This answers a question of Matet.

中文翻译：

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在 Con$(\mathfrak {d}_\lambda >\textrm {cov}_\lambda (\textrm {meagre}))$

我们证明了一致性：对于合适的强不可访问基数 lambda，支配数，即 ^{lambda}lambda 的共尾性，严格大于 cov_lambda(meagre)，即 ^{lambda}2 的最小无处稠密子集数需要覆盖它。这回答了 Matet 的问题。