Hypothesis: HR 41:
\(W_{\aleph _{1}}\): For every cardinal \(m\), \(m \le \aleph_{1}\) or \(\aleph_{1}\le m \).
Conclusion: HR 106:
Baire Category Theorem for Compact Hausdorff Spaces: Every compact Hausdorff space is Baire.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N16\) Jech/Levy/Pincus Model | \(A\) has cardinality \(\aleph_{\omega}\);\(\cal G\) is the group of all permutations on \(A\); and \(S\) is the set ofall subsets of \(A\) of cardinality less that \(\aleph_{\omega}\) |
Code: 5
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