We have the following indirect implication of form equivalence classes:
Implication | Reference |
---|---|
201 \(\Rightarrow\) 88 |
The dependence of some logical axioms on disjoint transversals and linked systems, Schrijver, A. 1978, Colloq. Math. |
88 \(\Rightarrow\) 276 |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
---|---|
201: | Linking Axiom for Boolean Algebras: Every Boolean algebra has a maximal linked system. (\(L\subseteq B\) is linked if \(a\wedge b\neq 0\) for all \(a\) and \(b \in L\).) |
88: | \(C(\infty ,2)\): Every family of pairs has a choice function. |
276: | \(E(V'',III)\): For every set \(A\), \({\cal P}(A)\) is Dedekind finite if and only if \(A = \emptyset\) or \(2|{\cal P}(A)| > |{\cal P}(A)|\). \ac{Howard/Spi\u siak} \cite{1994}. |
Comment: