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:

1 \(\Rightarrow\) 102 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
1 \(\Rightarrow\) 102

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

Howard-Rubin Number	Statement
1:	\(C(\infty,\infty)\):  The Axiom of Choice: Every  set  of  non-empty sets has a choice function.
102:	For all Dedekind finite cardinals \(p\) and \(q\), if \(p^{2} = q^{2}\) then \(p = q\). Jech [1973b], p 162 prob 11.12.

Comment: