Implications

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We have the following indirect implication of form equivalence classes:

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

Implication	Reference
295 \(\Rightarrow\) 30	"Dense orderings, partitions, and weak forms of choice", Gonzalez, C. 1995a, Fund. Math.

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

Howard-Rubin Number	Statement
295:	DO:  Every infinite set has a dense linear ordering.
30:	Ordering Principle: Every set can be linearly ordered.

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