Implications

We have the following indirect implication of form equivalence classes:

14 \(\Rightarrow\) 69
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
14 \(\Rightarrow\) 69 Algebraic closures without choice, Banaschewski, B. 1992, Z. Math. Logik Grundlagen Math.

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.

69:

Every field has an algebraic closure.  Jech [1973b], p 13.

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