Implications

We have the following indirect implication of form equivalence classes:

14 \(\Rightarrow\) 123
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
14 \(\Rightarrow\) 123 Variants of Rado's selection lemma and their applications, Rav, Y. 1977, Math. Nachr.

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.

123:

\(SPI^*\): Uniform weak ultrafilter principle: For each family \(F\) of infinite sets \(\exists f\) such that \(\forall x\in F\), \(f(x)\) is a non-principal ultrafilter on \(x\).

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