Statement:

\(DC(\aleph _{1})\):  Given a relation \(R\) such that for every  subset \(Y\) of a set \(X\) with \(|Y| < \aleph_{1}\) there is an \(x \in  X\)  with \(Y \mathrel R x\), then there is a function \(f: \aleph_{1} \rightarrow  X\) such that \((\forall\beta < \aleph_{1}) (\{f(\gamma ): \gamma < b \} \mathrel R f(\beta))\).

Howard_Rubin_Number: 44

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:
Levy-1964: The interdependence of certain consequences of the axiom of choice

Book references

Note connections:

The following forms are listed as conclusions of this form class in rfb1: 214, 43, 39, 40, 41, 44, 45-n, 67, 122, 152, 192, 193, 88, 327,

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