Implications

We have the following indirect implication of form equivalence classes:

39 \(\Rightarrow\) 380
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
39 \(\Rightarrow\) 8 clear
8 \(\Rightarrow\) 380 clear

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

Howard-Rubin Number Statement
39:

\(C(\aleph_{1},\infty)\): Every set \(A\) of non-empty sets such that \(\vert A\vert = \aleph_{1}\) has a choice function. Moore, G. [1982], p. 202.

8:

\(C(\aleph_{0},\infty)\):

380:

\(PC(\infty,WO,\infty)\):  For every infinite family of non-empty well orderable sets, there is an infinite subfamily \(Y\) of \(X\) which has a choice function.

Comment:

Back