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:

16 \(\Rightarrow\) 13 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
16 \(\Rightarrow\) 13	Zermelo's Axiom of Choice, Moore, [1982]

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

Howard-Rubin Number	Statement
16:	\(C(\aleph_{0},\le 2^{\aleph_{0}})\):  Every denumerable collection of non-empty sets  each with power \(\le  2^{\aleph_{0}}\) has a choice function.
13:	Every Dedekind finite subset of \({\Bbb R}\) is finite.

Comment: