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 \(\Rightarrow\) 140 | clear |
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. |
140: | Let \(\Omega\) be the set of all (undirected) infinite cycles of reals (Graphs whose vertices are real numbers, connected, no loops and each vertex adjacent to exactly two others). Then there is a function \(f\) on \(\Omega \) such that for all \(s\in\Omega\), \(f(s)\) is a direction along \(s\). |
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