We have the following indirect implication of form equivalence classes:
| Implication | Reference |
|---|---|
| 44 \(\Rightarrow\) 0 |
Here are the links and statements of the form equivalence classes referenced above:
| Howard-Rubin Number | Statement |
|---|---|
| 44: | \(DC(\aleph _{1})\): Given a relation \(R\) such that for every subset \(Y\) of a set \(X\) with \(|Y| < \aleph_{1}\) there is an \(x \in X\) with \(Y \mathrel R x\), then there is a function \(f: \aleph_{1} \rightarrow X\) such that \((\forall\beta < \aleph_{1}) (\{f(\gamma ): \gamma < b \} \mathrel R f(\beta))\). |
| 0: | \(0 = 0\). |
Comment: