Hypothesis: HR 6:
\(UT(\aleph_0,\aleph_0,\aleph_0,\Bbb R)\): The union of a denumerable family of denumerable subsets of \({\Bbb R}\) is denumerable.
Conclusion: HR 158:
In every Hilbert space \(H\), if the closed unit ball is sequentially compact, then \(H\) has an orthonormal basis.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N25\) Brunner's Model I | The set of atoms, \(A\), is equipped with thestructure of the Hilbert space \(\ell_2\), \(\cal G\) is the group of allpermutations on \(A\) that preserve the norm (unitary operators), and \(S\) isthe set of all finite subsets of \(A\) |
Code: 3
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