Statement:
\(C(\aleph_0,\aleph_0,\Bbb R)\): Every denumerable set of non-empty denumerable subsets of \({\Bbb R}\) has a choice function.
Howard_Rubin_Number: 5
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:
Sageev-1975: An independence result concerning the axiom of choice
Book references
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 5 A | Partial Choice for Countable Families of Countable Sets of Reals: Every countable family of non-empty countable sets of real numbers has an infinite subset with a choice function. (See the proof of the equivalence of 94 and [94 N].) \ac{Howard/Keremedis/Rubin/Stanley/Tachtsis} \cite{1999} \medskip |
|