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 46-K:
If \(K\) is a finite subset of \(\omega-\{0,1\}\), \(C(\infty,K)\): For every \(n\in K\), every set of \(n\)-element sets has a choice function.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N2(n)\) A generalization of \(\cal N2\) | This is a generalization of\(\cal N2\) in which there is a denumerable set of \(n\) element sets for\(n\in\omega - \{0,1\}\) |
| \(\cal N2(n,M)\) Mostowski's variation of \(\cal N2(n)\) | \(A\), \(B\), and \(S\)are the same as in \(\cal N2(n)\) |
Code: 3
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