Implications

We have the following indirect implication of form equivalence classes:

327 \(\Rightarrow\) 250
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
327 \(\Rightarrow\) 250 clear

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

Howard-Rubin Number Statement
327:

\(KW(WO,<\aleph_0)\),  The Kinna-Wagner Selection Principle for a well ordered family of finite sets: For every well ordered set \(M\) of finite sets there is a function \(f\) such that for all \(A\in M\), if \(|A|>1\)  then \(\emptyset\neq f(A)\subsetneq A\). (See Form 15.)

250:

\((\forall n\in\omega-\{0,1\})(C(WO,n))\): For every natural number \(n\ge 2\), every well ordered family of \(n\) element sets has a choice function.

Comment:

Back