We have the following indirect implication of form equivalence classes:
Implication | Reference |
---|---|
2 \(\Rightarrow\) 3 |
On successors in cardinal arithmetic, Truss, J. K. 1973c, Fund. Math. |
3 \(\Rightarrow\) 53 | note-68 |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
---|---|
2: | Existence of successor cardinals: For every cardinal \(m\) there is a cardinal \(n\) such that \(m < n\) and \((\forall p < n)(p \le m)\). |
3: | \(2m = m\): For all infinite cardinals \(m\), \(2m = m\). |
53: | For all infinite cardinals \(m\), \(m^2\le 2^m\). Mathias [1979], prob 1336. |
Comment: