Hypothesis: HR 31:
\(UT(\aleph_{0},\aleph_{0},\aleph_{0})\): The countable union theorem: The union of a denumerable set of denumerable sets is denumerable.
Conclusion: HR 27:
\((\forall \alpha)( UT(\aleph_{0},\aleph_{\alpha}, \aleph_{\alpha}))\): The union of denumerably many sets each of power \(\aleph_{\alpha }\) has power \(\aleph_{\alpha}\). Moore, G. [1982], p 36.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N17\) Brunner/Howard Model II | \(A=\{a_{\alpha,i}:\alpha\in\omega_1\,\wedge i\in\omega\}\) |
Code: 3
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