Implications

We have the following indirect implication of form equivalence classes:

211 \(\Rightarrow\) 13
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
211 \(\Rightarrow\) 13 clear

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
211:

\(DCR\): Dependent choice for relations on \(\Bbb R\): If \(R\subseteq\Bbb R\times\Bbb R\) satisfies \((\forall x\in \Bbb R)(\exists y\in\Bbb R)(x\mathrel R y)\) then there is a sequence \(\langle x(n): n\in\omega\rangle\) of real numbers such that \((\forall n\in\omega)(x(n)\mathrel R x(n+1))\).

13:

Every Dedekind finite subset of \({\Bbb R}\) is finite.

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