Hypothesis: HR 3: \(2m = m\): For all infinite cardinals \(m\), \(2m = m\).
Conclusion: HR 15:
\(KW(\infty,\infty)\) (KW), The Kinna-Wagner Selection Principle: For every set \(M\) there is a function \(f\) such that for all \(A\in M\), if \(|A|>1\) then \(\emptyset\neq f(A)\subsetneq A\). (See Form 81(\(n\)).
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N9\) Halpern/Howard Model | \(A\) is a set of atoms with the structureof the set \( \{s : s:\omega\longrightarrow\omega \wedge (\exists n)(\forall j > n)(s_j = 0)\}\) |
Code: 5
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