We have the following indirect implication of form equivalence classes:
Implication | Reference |
---|---|
85 \(\Rightarrow\) 32 | clear |
32 \(\Rightarrow\) 10 | clear |
10 \(\Rightarrow\) 249 |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
---|---|
85: | \(C(\infty,\aleph_{0})\): Every family of denumerable sets has a choice function. Jech [1973b] p 115 prob 7.13. |
32: | \(C(\aleph_0,\le\aleph_0)\): Every denumerable set of non-empty countable sets has a choice function. |
10: | \(C(\aleph_{0},< \aleph_{0})\): Every denumerable family of non-empty finite sets has a choice function. |
249: | If \(T\) is an infinite tree in which every element has exactly 2 immediate successors then \(T\) has an infinite branch. |
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