Implications

We have the following indirect implication of form equivalence classes:

295 \(\Rightarrow\) 377
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.
30 \(\Rightarrow\) 377 clear

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.

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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