Hypothesis: HR 39:
\(C(\aleph_{1},\infty)\): Every set \(A\) of non-empty sets such that \(\vert A\vert = \aleph_{1}\) has a choice function. Moore, G. [1982], p. 202.
Conclusion: HR 388:
Every infinite branching poset (a partially ordered set in which each element has at least two lower bounds) has either an infinite chain or an infinite antichain.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N21(\aleph_{\alpha+1})\) Jensen's Model | We assume \(\aleph_{\alpha+1}\) is a regular cardinal |
Code: 3
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