Implications

We have the following indirect implication of form equivalence classes:

132 \(\Rightarrow\) 342-n
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
132 \(\Rightarrow\) 342-n clear

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

Howard-Rubin Number Statement
132:

\(PC(\infty, <\aleph_0,\infty)\):  Every infinite family of finite  sets has an infinite subfamily with a choice function.

342-n:

(For \(n\in\omega\), \(n\ge 2\).) \(PC(\infty,n,\infty)\):  Every infinite family of \(n\)-element sets has an infinite subfamily with a choice function. (See Form 166.)

Comment:

Back