We have the following indirect implication of form equivalence classes:
Implication | Reference |
---|---|
86-alpha \(\Rightarrow\) 8 | clear |
8 \(\Rightarrow\) 421 |
Unions and the axiom of choice, De-la-Cruz-Hall-Howard-Keremedis-Rubin-2002B[2002B], Math. Logic Quart. |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
---|---|
86-alpha: | \(C(\aleph_{\alpha},\infty)\): If \(X\) is a set of non-empty sets such that \(|X| = \aleph_{\alpha }\), then \(X\) has a choice function. |
8: | \(C(\aleph_{0},\infty)\): |
421: | \(UT(\aleph_0,WO,WO)\): The union of a denumerable set of well orderable sets can be well ordered. |
Comment: