All Questions

We say that $A\subseteq \omega$ is a nullset if $$\lim\sup_{n\to \infty} \frac{|A\cap n|}{n+1} = 0.$$ Let $\omega^\omega$ denote the set of functions $f:\omega\to\omega$. We define a pre-ordering ...

The mod finite order on ${}^\omega \omega$ is defined as $f \leq^\ast g$ if and only if $f(n) \leq g(n)$ except for finitely many $n \in \omega$. My question is: can we always extract a cofinal well-...

Suppose $(P, <)$ is a poset of cofinality $\aleph_2$ and additivity (least cardinality of an unbounded subset) $\aleph_1$. Can we conclude the existence of a cofinal subset of order-type $\omega_1 \...

This question branches from Taras Banakh's recent question on a cardinal characteristic connected to families of partitions that are directed in the ordering of partition refinement. A partition $\...