We have the following indirect implication of form equivalence classes:
Implication | Reference |
---|---|
385 \(\Rightarrow\) 70 | note-150 |
70 \(\Rightarrow\) 93 | The Axiom of Choice, Jech, 1973b, page 7 problem 10 |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
---|---|
385: | Countable Ultrafilter Theorem: Every proper filter with a countable base over a set \(S\) (in \({\cal P}(S)\)) can be extended to an ultrafilter. |
70: | There is a non-trivial ultrafilter on \(\omega\). Jech [1973b], prob 5.24. |
93: | There is a non-measurable subset of \({\Bbb R}\). |
Comment: