We have the following indirect implication of form equivalence classes:
Implication | Reference |
---|---|
71-alpha \(\Rightarrow\) 9 | clear |
9 \(\Rightarrow\) 342-n | clear |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
---|---|
71-alpha: | \(W_{\aleph_{\alpha}}\): \((\forall x)(|x|\le\aleph_{\alpha }\) or \(|x|\ge \aleph_{\alpha})\). Jech [1973b], page 119. |
9: | Finite \(\Leftrightarrow\) Dedekind finite: \(W_{\aleph_{0}}\) Jech [1973b]: \(E(I,IV)\) Howard/Yorke [1989]): Every Dedekind finite set is finite. |
342-n: | (For \(n\in\omega\), \(n\ge 2\).) \(PC(\infty,n,\infty)\): Every infinite family of \(n\)-element sets has an infinite subfamily with a choice function. (See Form 166.) |
Comment: