Implications

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We have the following indirect implication of form equivalence classes:

9 \(\Rightarrow\) 13 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
9 \(\Rightarrow\) 13	clear

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

Howard-Rubin Number	Statement
9:	Finite \(\Leftrightarrow\) Dedekind finite: \(W_{\aleph_{0}}\) Jech [1973b]: \(E(I,IV)\) Howard/Yorke [1989]): Every Dedekind finite set is finite.
13:	Every Dedekind finite subset of \({\Bbb R}\) is finite.

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