Hypothesis: HR 0: \(0 = 0\).
Conclusion: HR 209:
There is an ordinal \(\alpha\) such that for all \(X\), if \(X\) is a denumerable union of denumerable sets then \({\cal P}(X)\) cannot be partitioned into \(\aleph_{\alpha}\) non-empty sets.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M28\) Morris' Model II | Morris constructs a generic extension of acountable standard model of ZFC in which there is a proper class ofgeneric sets |
Code: 3
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