We have the following indirect implication of form equivalence classes:
Implication | Reference |
---|---|
344 \(\Rightarrow\) 62 | clear |
62 \(\Rightarrow\) 102 | The Axiom of Choice, Jech, 1973b, page 162 problem 11.12 |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
---|---|
344: | If \((E_i)_{i\in I}\) is a family of non-empty sets, then there is a family \((U_i)_{i\in I}\) such that \(\forall i\in I\), \(U_i\) is an ultrafilter on \(E_i\). |
62: | \(C(\infty,< \aleph_{0})\): Every set of non-empty finite sets has a choice function. |
102: | For all Dedekind finite cardinals \(p\) and \(q\), if \(p^{2} = q^{2}\) then \(p = q\). Jech [1973b], p 162 prob 11.12. |
Comment: