Implications

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We have the following indirect implication of form equivalence classes:

90 \(\Rightarrow\) 51 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
90 \(\Rightarrow\) 51	Variations of Zorn's lemma, principles of cofinality, and Hausdorff's maximal principle, Part I and II, Harper, J. 1976, Notre Dame J. Formal Logic

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

Howard-Rubin Number	Statement
90:	\(LW\):  Every linearly ordered set can be well ordered. Jech [1973b], p 133.
51:	Cofinality Principle: Every linear ordering has a cofinal sub well ordering.  Sierpi\'nski [1918], p 117.

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