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 238:
Every elementary Abelian group (that is, for some prime \(p\) every non identity element has order \(p\)) is the direct sum of cyclic subgroups.
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: