Implications

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We have the following indirect implication of form equivalence classes:

30 \(\Rightarrow\) 377 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
30 \(\Rightarrow\) 377	clear

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

Howard-Rubin Number	Statement
30:	Ordering Principle: Every set can be linearly ordered.
377:	Restricted Ordering Principle:  For every infinite set \(X\) there is an infinite subset \(Y\) of \(X\) such that \(Y\) can be linearly ordered.

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