We have the following indirect implication of form equivalence classes:

101 \(\Rightarrow\) 101
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
101 \(\Rightarrow\) 101 Sur une proposition qui entraine l'existence des ensembles non mesurables, Sierpi'nski, W. 1947, Fund. Math.

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

Howard-Rubin Number Statement
101:

Partition Principle:  If \(S\) is a partition of \(M\), then \(S \precsim M\).

101:

Partition Principle:  If \(S\) is a partition of \(M\), then \(S \precsim M\).

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