Hypothesis: HR 313:
\(\Bbb Z\) (the set of integers under addition) is amenable. (\(G\) is {\it amenable} if there is a finitely additive measure \(\mu\) on \(\cal P(G)\) such that \(\mu(G) = 1\) and \(\forall A\subseteq G, \forall g\in G\), \(\mu(gA)=\mu(A)\).)
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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