On CON(${\mathfrak d}_λ>$ cov$_λ$(meagre))

On CON(Dominating_lambda > cov_λ(meagre))

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(meagre_lambda), i.e. the minimal number of nowhere dense subsets of 2^lambda needed to cover it. This answers a question of Matet.

Consistency of "the ideal of null restricted to some A is kappa-complete not kappa^+-complete, kappa weakly inaccessible and cov(meagre)=aleph_1"

In this note we answer the following question of Grinblat: Is it consistent that for some set X, cov(NULL restriction X)=lambda is a weakly inaccessible cardinal (so X not null of course) while cov(meagre) is small, say it is aleph_1.

Possibly every real function is continuous on a non--meagre set

We prove consistency of the following sentence: ``ZFC + every real function is continuous on a non-meagre set'', answering a question of Fremlin.

The number of translates of a closed nowhere dense set required to cover a Polish group

For a Polish group G let cov_G be the minimal number of translates of a fixed closed nowhere dense subset of G required to cover G. For many locally compact G this cardinal is known to be consistently larger than cov(meager) which is the smallest cardinality of a covering of the real line by meagre sets. It is shown that for several non-locally compact groups cov_G=cov(meager). For example the equality holds for the group of permutations of the integers, the additive group of a separable Banach space with an unconditional basis and the group of homeomorphisms of various compact spaces. Most re…

不可达基数下随机实数力迫的推广

Generalizing random real forcing for inaccessible cardinals

本文针对不可达基数$\u03bb$对应的$\u03bb^\u03bb$空间，在附加假设下构造了具备随机实数力迫性质的推广力迫，证明其保持基数与共尾性且不添加无支配实数，填补了随机实数力迫在高阶无穷空间的推广空白。

书法有关偶然编纂的基数特征比较

Calligraphy Concerning Casually Compiled Cardinal Characteristic Comparisons

本文建立了连续体基数特征的不等式，探讨了分拆分裂数与稀疏理想统一性、实数集的强测度零性质、统计性驱逐数与实数覆盖的关系，以及各类基数特征间的比较。