Implications

We have the following indirect implication of form equivalence classes:

269 \(\Rightarrow\) 269
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
269 \(\Rightarrow\) 269

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

Howard-Rubin Number Statement
269:

For every cardinal \(m\), there is a set \(A\) such that \(2^{|A|^2}\ge m\) and there is a choice function on the collection of 2-element subsets of \(A\).

269:

For every cardinal \(m\), there is a set \(A\) such that \(2^{|A|^2}\ge m\) and there is a choice function on the collection of 2-element subsets of \(A\).

Comment:

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