Hypothesis: HR 116:
Every compact \(T_2\) space is weakly Loeb. Weakly Loeb means the set of non-empty closed subsets has a multiple choice function.
Conclusion: HR 200:
For all infinite \(x\), \(|2^{x}| = |x!|\).
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N1\) The Basic Fraenkel Model | The set of atoms, \(A\) is denumerable; \(\cal G\) is the group of all permutations on \(A\); and \(S\) isthe set of all finite subsets of \(A\) |
Code: 5
Comments: