Hypothesis: HR 23:
\((\forall \alpha)(UT(\aleph_{\alpha},\aleph_{\alpha}, \aleph_{\alpha}))\): For every ordinal \(\alpha\), if \(A\) and every member of \(A\) has cardinality \(\aleph_{\alpha}\), then \(|\bigcup A| = \aleph _{\alpha }\).
Conclusion: HR 124:
Every operator on a Hilbert space with an amorphous base is the direct sum of a finite matrix and a scalar operator. (A set is amorphous if it is not the union of two disjoint infinite sets.)
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N24\) Hickman's Model I | This model is a variation of \(\cal N2\) |
Code: 5
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