Statement:
\(C(WO,\infty)\): Every well orderable set of non-empty sets has a choice function. Moore, G. [1982], p 325.
Howard_Rubin_Number: 40
Parameter(s): This form does not depend on parameters
This form's transferability is: Transferable
This form's negation transferability is: Negation Transferable
Article Citations:
Book references
Zermelo's Axiom of Choice, Moore, G.H., 1982
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 40 A | \(A(L2,L1)\): For every \(T_2\) topological space \((X,T)\), if each open cover of \(X\) has a well ordered subcover, then each open cover has a well ordered refinement. |
Brunner [1983d]
Note [26] |
| 40 B | For all ordinals \(\alpha\), the \(\aleph_{\alpha}\) partition principle holds: For every ordinal \(\alpha\) and every cardinal \(\kappa\), if \(\aleph_{\alpha}\le^* \kappa\), then \(\aleph_{\alpha} \le\kappa\). |
Pelc [1978]
Banaschewski-Moore-1990
Note [69] |
| 40 C | For each idemmultiple set \(x\) (\(2\times x\approx x\)), if there exists a surjection \(f\) mapping \(x\) onto an ordinal \(\lambda\) such that for each \(\psi < \lambda\), \(f^{-1}[\{\psi\}]\) is Dedekind infinite, then \(\lambda \precsim x\). |
Higasikawa [1995]
Note [94] |