Implications

We have the following indirect implication of form equivalence classes:

168 \(\Rightarrow\) 100
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
168 \(\Rightarrow\) 100 clear

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

Howard-Rubin Number Statement
168:

Dual Cantor-Bernstein Theorem:\((\forall x) (\forall y)(|x| \le^*|y|\) and \(|y|\le^* |x|\) implies  \(|x| = |y|)\) .

100:

Weak Partition Principle:  For all sets \(x\) and \(y\), if \(x\precsim^* y\), then it is not the case that \(y\prec x\).

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