Statement:
\(UT(\aleph_0,n,\aleph_0)\) for \(n\in\omega -\{0,1\}\): The union of a denumerable set of \(n\)-element sets is denumerable.
Howard_Rubin_Number: 374-n
Parameter(s): This form depends on the following parameter(s): \(n\),
This form's transferability is: Transferable
This form's negation transferability is: Negation Transferable
Article Citations:
Book references
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 374 A-n | For each \(i\), \(2\le i\le n\in\omega-\{0,1\}\). \(C(\aleph_0,i)\): Every denumerable set of \(i\)-element sets has a choice function. |
|
| 374 B-n+1 | Countable products of Hausdorff spaces \(X_m\), with \(|X_m|\leq n+1\), \(m\in\omega\), are compact. |
Herrlich-Keremedis-1999b
|
| 374 C n+1 | Countable products of Hausdorff spaces \(X_m\), with \(|X_m|\leq n+1\), \(m\in\omega\), are Baire. |
Herrlich-Keremedis-1999b
Note [28] |
| 374 D-n | \(UT(\aleph_0,n,WO)\), \(n\in\omega-\{0,1\}\): The union of a denumerable set of \(n\)-element sets can be well ordered. |
|