Implications

We have the following indirect implication of form equivalence classes:

51 \(\Rightarrow\) 77
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
51 \(\Rightarrow\) 77 Well ordered subsets of linearly ordered sets, Howard, P. 1994, Notre Dame J. Formal Logic

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

Howard-Rubin Number Statement
51:

Cofinality Principle: Every linear ordering has a cofinal sub well ordering.  Sierpi\'nski [1918], p 117.

77:

A linear ordering of a set \(P\) is a well ordering if and only if \(P\) has no infinite descending sequences. Jech [1973b], p 23.

Comment:

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