Implications

• Implications Home
• Code 1 Implications
• Code 2 Implications
• Code 3 Implications
• Code 4 Implications
• Code 5 Implications
• Code 6 Implications
• Complete List
• Search

We have the following indirect implication of form equivalence classes:

91 \(\Rightarrow\) 38 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
91 \(\Rightarrow\) 37	Equivalents of the Axiom of Choice II, Rubin, 1985, theorem 5.7
37 \(\Rightarrow\) 38	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.

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

Howard-Rubin Number	Statement
91:	\(PW\):  The power set of a well ordered set can be well ordered.
37:	Lebesgue measure is countably additive.
38:	\({\Bbb R}\) is not the union of a countable family of countable sets.

Comment: