Hypothesis: HR 71-alpha:
\(W_{\aleph_{\alpha}}\): \((\forall x)(|x|\le\aleph_{\alpha }\) or \(|x|\ge \aleph_{\alpha})\). Jech [1973b], page 119.
Conclusion: HR 8:
\(C(\aleph_{0},\infty)\):
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N16(\aleph_{\gamma})\) Levy's Model II | This is an extension of\(\cal N16\) in which \(A\) has cardinality \(\aleph_{\gamma}\) wherecf\((\aleph_{\gamma}) = \aleph_0\); \(\cal G\) is the group of allpermutations on \(A\); and \(S\) is the set of all subsets of \(A\) ofcardinality less that \(\aleph_{\gamma}\) |
Code: 3
Comments: