Form equivalence class Howard-Rubin Number: 1
Statement:
For all ordinals \(\alpha\), \(DC(\aleph_{\alpha})\): Given a relation \(R\) such that for every subset \(Y\) of a set \(X\) with\(|Y| < \aleph_{\alpha}\), there is an \(x \in X \) with \(Y\mathrel R x\), then there is a function \(f:\aleph_{\alpha} \to X\) such that \(\forall\beta < \aleph_{\alpha}\), \(\{f(\gamma):\gamma < \beta\}\mathrel Rf(\beta)\).
Howard-Rubin number: 1 F
Citations (articles):
Levy [1964]
The interdependence of certain consequences of the axiom of choice
Connections (notes): Note [133]
Prove forms [1 F] and [1 CC] are equivalent to Form 1
References (books):
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