claytonhida

Irredundant sets

Parte 1 – Irredundance for Boolean algebras.

Definition: Let A be a Boolean algebra. A set \mathcal{F}\subseteq \mathcal{A} is an irredundant set if and only if for every a\in \mathcal{F}, a  does not belong to the Boolean subalgebra generated by \mathcal{F}\setminus\{a\}. We define

irr(\mathcal{A}):=\sup\{|\mathcal{F}|: \mathcal{F} \textrm{ is irredundant}\}

From the definition it follows that

irr(\mathcal{A})\leq |\mathcal{A}|

for every Boolean algebra \mathcal{A}.

One of the interesting questions is about the possible gap between irr(A) and |\mathcal{A}|.

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