Hypothesis: HR 60:
\(C(\infty,WO)\): Every set of non-empty, well orderable sets has a choice function.
Moore, G. [1982], p 125.
Conclusion: HR 65:
The Krein-Milman Theorem: Let \(K\) be a compact convex set in a locally convex topological vector space \(X\). Then \(K\) has an extreme point. (An extreme point is a point which is not an interior point of any line segment which lies in \(K\).) Rubin, H./Rubin, J. [1985] p. 177.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M1\) Cohen's original model | Add a denumerable number of generic reals (subsets of \(\omega\)), \(a_1\), \(a_2\), \(\cdots\), along with the set \(b\) containing them |
Code: 3
Comments: