Axiom Of Choice

We have the following indirect implication of form equivalence classes:

303 \(\Rightarrow\) 303 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
303 \(\Rightarrow\) 303

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number	Statement
303:	If \(B\) is a Boolean algebra, \(S\subseteq B\) and \(S\) is closed under \(\land\), then there is a \(\subseteq\)-maximal proper ideal \(I\) of \(B\) such that \(I\cap S= \{0\}\).
303:	If \(B\) is a Boolean algebra, \(S\subseteq B\) and \(S\) is closed under \(\land\), then there is a \(\subseteq\)-maximal proper ideal \(I\) of \(B\) such that \(I\cap S= \{0\}\).

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