Almost Disjoint and Mad Families in Vector Spaces and Choice Principles

Journal of Symbolic Logic 87 (3):1093-1110 (2022)
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In set theory without the Axiom of Choice ( $\mathsf {AC}$ ), we investigate the open problem of the deductive strength of statements which concern the existence of almost disjoint and maximal almost disjoint (MAD) families of infinite-dimensional subspaces of a given infinite-dimensional vector space, as well as the extension of almost disjoint families in infinite-dimensional vector spaces to MAD families.



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MA(ℵ0) restricted to complete Boolean algebras and choice.Eleftherios Tachtsis - 2021 - Mathematical Logic Quarterly 67 (4):420-431.
No decreasing sequence of cardinals.Paul Howard & Eleftherios Tachtsis - 2016 - Archive for Mathematical Logic 55 (3-4):415-429.
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