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 96:
Löwig's Theorem:If \(B_{1}\) and \(B_{2}\) are both bases for the vector space \(V\) then \(|B_{1}| = |B_{2}|\).
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N13\) L\"auchli/Jech Model | \(A = B_1\cup B_2\), where \(B_1=\bigcup\{A_{j1} : j\in\omega\}\), and \(B_2 = \bigcup\{A_{j2} :j\in\omega\}\), and each \(A_{ji}\) is a 6-element set |
Code: 3
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