Statement:
(For \(n\in\omega\), \(n\ge 2\).) \(PC(\aleph_0,n,\infty)\): Every denumerable set of \(n\)-element sets has an infinite subset with a choice function.
Howard_Rubin_Number: 373-n
Parameter(s): This form depends on the following parameter(s): \(q\), \(k\): integer \( > 1 \)
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 |
|---|---|---|
| 373 A-n | (For \(n\in\omega\), \(n\ge 2\).) \(PC(WO,n,\infty)\): Every infinite well ordered set of \(n\)-element sets has an infinite subset with a choice function. |
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| 373 B-n | \(PUT(\aleph_0,n,\aleph_0)\) for \(n\in\omega-\{0,1\}\): The union of a denumerable set of pairwise disjoint \(n\)-element sets has a denumerable subset. |
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| 373 C-n | \(PUT(WO,n,WO)\) for \(n\in\omega -\{0,1\}\): The union of an infinite well ordered set of pairwise disjoint \(n\)-element sets has an infinite well ordered subset. |
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| 373 D-n | \(PUT(\aleph_0,n,WO)\) for \(n\in\omega -\{0,1\}\): The union of a denumerable set of pairwise disjoint \(n\)-element sets has an infinite well ordered subset |
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