Statement:
\(PC(\infty, <\aleph_0,\infty)\): Every infinite family of finite sets has an infinite subfamily with a choice function.
Howard_Rubin_Number: 132
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:
Blass-1977a: Ramsey's theorem in the hierarchy of choice principles
Kleinberg-1969: The independence of Ramsey's theorem
Book references
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 132 A | Every set mapping \(f: X\rightarrow [X]^{WO}\) (well orderable subsets of \(X\)) on a Dedekind finite, infinite set \(X\) has an infinite free subset. |
Brunner [1989]
Note [22] Note [94] |