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ALMOST DISJOINT AND MAD FAMILIES IN VECTOR SPACES AND CHOICE PRINCIPLES
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 87 / Issue 3 / September 2022
- Published online by Cambridge University Press:
- 29 October 2021, pp. 1093-1110
- Print publication:
- September 2022
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- Article
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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.
