Form equivalence class Howard-Rubin Number: 106

Statement:

Weak DC: If \(R\) is a binary relation on a non-empty set \(E\) such that \((\forall x\in E)(\exists y\in E)( x\mathrel R y)\), then there is a sequence \(\langle F_n\rangle_{n\in\omega}\) of non-empty finite subsets of \(E\) such that \((\forall n\in\omega) (\forall x\in F_n)(\exists y\in F_{n+1}) (x\mathrel R y)\). (This statement remains equivalent to Form 106 if we replace "binary relation" by "transitive binary relation".)

Howard-Rubin number: 106 B

Citations (articles): Fossy/Morillon [1998] The Baire category property and some notions of compactness

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