Implications

We have the following indirect implication of form equivalence classes:

101 \(\Rightarrow\) 93
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
101 \(\Rightarrow\) 93 L’axiome de M. Zermelo et son rˆole dans la th´eorie des ensembles et l’analyse, Sierpi'nski, W. 1918, Bull. Int. Acad. Sci. Cracovie Cl. Math. Nat.
Sur une proposition qui entraine l'existence des ensembles non mesurables, Sierpi'nski, W. 1947, Fund. Math.
Zermelo's Axiom of Choice, Moore, [1982]

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 \(S \precsim M\).

93:

There is a non-measurable subset of \({\Bbb R}\).

Comment:

Back