Hypothesis: HR 345:
Rasiowa-Sikorski Axiom: If \((B,\land,\lor)\) is a Boolean algebra, \(a\) is a non-zero element of \(B\), and \(\{X_n: n\in\omega\}\) is a denumerable set of subsets of \(B\) then there is a maximal filter \(F\) of \(B\) such that \(a\in F\) and for each \(n\in\omega\), if \(X_n\subseteq F\) and \(\bigwedge X_n\) exists then \(\bigwedge X_n \in F\).
Conclusion: HR 328:
\(MC(WO,\infty)\): For every well ordered set \(X\) such that for all \(x\in X\), \(|x|\ge 1\), there is a function \(f\) such that and for every \(x\in X\), \(f(x)\) is a finite, non-empty subset of \(x\). (See Form 67.)
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N40\) Howard/Rubin Model II | A variation of \(\cal N38\) |
Code: 5
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