Irredundant sets in Boolean algebras

Todorčević, Stevo

doi:10.1090/S0002-9947-1993-1080736-3

Irredundant sets in Boolean algebras
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by Stevo Todorčević

Trans. Amer. Math. Soc. 339 (1993), 35-44

DOI: https://doi.org/10.1090/S0002-9947-1993-1080736-3

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Abstract:

It is shown that every uncountable Boolean algebra $A$ contains an uncountable subset $I$ such that no $a$ of $I$ is in the subalgebra generated by $I\backslash \{ a\}$ using an additional axiom of set theory. It is also shown that a use of some such axiom is necessary.

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