2 problems

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Semiproximality criterion for real-embeddable almost disjoint families
Semiproximality conjecture. An $$ -embeddable almost disjoint family is semiproximal if and only if the range of some (equivalently, every) embedding contains no uncountable perfec…
Conjectureopenalmost-disjoint-families semiproximality topological-groupsarXiv posted 2 days ago
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The splitting number as the least size of a non-fin-intersecting almost disjoint family
Splitting-number conjecture. The cardinal $\mathfrak{s}$ is the first cardinal $\kappa$ for which there exists a non-fin-intersecting almost disjoint family of size $\kappa$ ; equiv…
Conjectureopenalmost-disjoint-families cardinal-characteristics set-theoryarXiv posted 2 days ago

Semiproximality criterion for real-embeddable almost disjoint families