We have the following indirect implication of form equivalence classes:
| Implication | Reference |
|---|---|
| 129 \(\Rightarrow\) 129 |
Realisierung und Auswahlaxiom, Brunner, N. 1984f, Arch. Math. (Brno) |
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 \(\omega^* + \omega\).) |
| 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 \(\omega^* + \omega\).) |
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