Hypothesis: HR 305:
There are \(2^{\aleph_0}\) Vitali equivalence classes. (Vitali equivalence classes are equivalence classes of the real numbers under the relation \(x\equiv y\leftrightarrow(\exists q\in{\Bbb Q})(x-y=q)\).). \ac{Kanovei} \cite{1991}.
Conclusion: HR 237:
The order of any group is divisible by the order of any of its subgroups, (i.e., if \(H\) is a subgroup of \(G\) then there is a set \(A\) such that \(|H\times A| = |G|\).)
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N32\) Hickman's Model III | This is a variation of \(\cal N1\) |
Code: 3
Comments: