Hypothesis: HR 361:
In \(\Bbb R\), the union of a denumerable number of analytic sets is analytic. G. Moore [1982], pp 181 and 325.
Conclusion: HR 235:
If \(V\) is a vector space and \(B_{1}\) and \(B_{2}\) are bases for \(V\) then \(|B_{1}|\) and \(|B_{2}|\) are comparable.
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
Comments: