Hypothesis: HR 15:
\(KW(\infty,\infty)\) (KW), The Kinna-Wagner Selection Principle: For every set \(M\) there is a function \(f\) such that for all \(A\in M\), if \(|A|>1\) then \(\emptyset\neq f(A)\subsetneq A\). (See Form 81(\(n\)).
Conclusion: HR 213:
\(C(\infty,\aleph_{1})\): If \((\forall y\in X)(|y| = \aleph_{1})\) then \(X\) has a choice function.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M34(\aleph_1)\) Pincus' Model III | Pincus proves that Cohen's model <a href="/models/Cohen-1">\(\cal M1\)</a> can be extended by adding \(\aleph_1\) generic sets along with the set \(b\) containing them and well orderings of all countable subsets of \(b\) |
Code: 3
Comments: