Implications

We have the following indirect implication of form equivalence classes:

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

Implication Reference
15 \(\Rightarrow\) 295 The dense linear ordering principle, Pincus, D. 1997, J. Symbolic Logic

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

Howard-Rubin Number Statement
15:

\(KW(\infty,\infty)\) (KW), The Kinna-Wagner Selection Principle: For every  set \(M\) there is a function \(f\) such that for all \(A\in M\), if \(|A|>1\) then \(\emptyset\neq f(A)\subsetneq A\). (See Form 81(\(n\)).  

295:

DO:  Every infinite set has a dense linear ordering.

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