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 220-p:
Suppose \(p\in\omega\) and \(p\) is a prime. Any two elementary Abelian \(p\)-groups (all non-trivial elements have order \(p\)) of the same cardinality are isomorphic.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N42(p)\) Hickman's Model IV | This model is an extension of \(\cal N32\) |
| \(\cal N45(p)\) Howard/Rubin Model III | Let \(p\) be a prime |
Code: 3
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