8 problems

Let $\mathfrak s$ and $\mathfrak r$ denote the splitting and reaping numbers, and let $\mathfrak c$ denote the continuum. Consider models obtained by the shattered iteration of eit…

Let $\mathfrak b$, $\mathfrak d$, and $\mathfrak c$ denote the bounding number, dominating number, and continuum, respectively. Assume … and let $\kappa,\lambda$ be regular cardina…

Dualization conjecture.

Let ${\mathsf{all}}$ be the ambient parameter set, and let $X,X'\subseteq{\mathsf{all}}$ satisfy … Let $Y$ be arbitrary, and write ${\mathfrak{dd}}_{X,Y}$ for the associated densit…

For $r\in(0,1)$, let ${\mathfrak{dd}}_{\{r\},{\mathsf{all}}}$ denote the corresponding density cardinal; the same notation is used when ${\mathsf{all}}$ is replaced by $[0,1]$,…

Partial-slalom separation conjecture.

Consistency conjecture. There exists a model $\bo\mathbf V$ such that

Let $\mathcal{I}$ be a fragmented ideal. The associated Rothberger number $\mathfrak{b}(\mathcal{I})$ is the least size of a family witnessing the corresponding Rothberger property…