Existence of Sacks-indestructible MAD families below ω{\aleph}_{\omega}

From papers

Let s\mathfrak{s} be the splitting number and b\mathfrak{b} the bounding number. A Sacks-indestructible MAD family is a maximal almost disjoint family that remains maximal after forcing with Sacks forcing.

Sacks-indestructibility conjecture. If

sb<ω,\mathfrak{s}\leq\mathfrak{b}<\aleph_{\omega},

then there is a Sacks-indestructible MAD family.

This conjecture links the cardinal-invariant inequality sb\mathfrak{s}\leq\mathfrak{b} below ω\aleph_{\omega} with preservation of maximal almost disjointness under Sacks forcing. The paper states the existence claim but does not provide a proof or resolution.

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Sources & referencesView supporting material

Primary source

Dilip Raghavan and Juris Steprāns, “On weakly tight families”, arXiv:1010.1226 (2010).

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