Implications

We have the following indirect implication of form equivalence classes:

14 \(\Rightarrow\) 141
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
14 \(\Rightarrow\) 141 Generalizing Konigs infinity lemma, Cowen, R.H. 1977b, Notre Dame J. Formal Logic

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

Howard-Rubin Number Statement
14:

BPI: Every Boolean algebra has a prime ideal.

141:

[14 P(\(n\))] with \(n = 2\):  Let \(\{A(i): i\in I\}\) be a collection of sets such that \(\forall i\in I,\ |A(i)|\le 2\) and suppose \(R\) is a symmetric binary relation on \(\bigcup^{}_{i\in I} A(i)\) such that for all finite \(W\subseteq I\) there is an \(R\) consistent choice function for \(\{A(i): i \in W\}\). Then there is an \(R\) consistent choice function for \(\{A(i): i\in I\}\).

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