Statement:
\(PUT(\aleph_{0},2,\aleph_{0})\): The union of a denumerable family of pairwise disjoint pairs has a denumerable subset.
Howard_Rubin_Number: 18
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:
Brunner-1984f: Realisierung und Auswahlaxiom
Book references
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 18 A | \(PC(\aleph_{0},2,\infty)\): Every denumerable setof pairs has an infinite subset with a choice function. |
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| 18 B | PUT(\(\aleph_0\),2,WO): The union of adenumerable family of pairs has an infinite well ordered subset. (18 \(\to\) [18 B] \(\to\)[18 A]) |
|
| 18 C | \(PC(WO,2,\infty)\): Every infinite well orderedset of pairs has an infinite subset with a choice function. |
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| 18 D | \(PUT(WO,2,WO)\): The union of an infinite well orderedfamily of pairwise disjoint pairs has an infinite well ordered subset.([18 D \(\leftrightarrow\) 18) |
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