We have the following indirect implication of form equivalence classes:
| Implication | Reference |
|---|---|
| 129 \(\Rightarrow\) 0 |
Here are the links and statements of the form equivalence classes referenced above:
| Howard-Rubin Number | Statement |
|---|---|
| 129: | For every infinite set \(A\), \(A\) admits a partition into sets of order type \(\omega^{*} + \omega\). (For every infinite \(A\), there is a set \(\{\langle C_j,<_j \rangle: j\in J\}\) such that \(\{C_j: j\in J\}\) is a partition of \(A\) and for each \(j\in J\), \(<_j\) is an ordering of \(C_j\) of type \(\omega^* + \omega\).) |
| 0: | \(0 = 0\). |
Comment: