Hypothesis: HR 8:
\(C(\aleph_{0},\infty)\):
Conclusion: HR 110:
Every vector space over \(\Bbb Q\) has a basis.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N2(\aleph_{\alpha})\) Jech's Model | This is an extension of \(\cal N2\) in which \(A=\{a_{\gamma} : \gamma\in\omega_{\alpha}\}\); \(B\) is the corresponding set of \(\aleph_{\alpha}\) pairs of elements of \(A\); \(\cal G\)is the group of all permutations on \(A\) that leave \(B\) point-wise fixed;and \(S\) is the set of all subsets of \(A\) of cardinality less than\(\aleph_{\alpha}\) |
Code: 3
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