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 136-k:
Surjective Cardinal Cancellation (depends on \(k\in\omega-\{0\}\)): For all cardinals \(x\) and \(y\), \(kx\le^* ky\) implies \(x\le^* y\).
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N20\) Truss' Model II | <p> Let \(X=\{a(i,k,l): i\in 2, k\in \Bbb Z, l\in\omega\}\), \(Y=\{a(i,j,k,l): i,j\in 2, k\in\Bbb Z, i\in\omega\}\) and \(A\) is the disjoint union of \(X\) and \(Y\) </p> |
Code: 3
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