Hypothesis: HR 295:
DO: Every infinite set has a dense linear ordering.
Conclusion: HR 384:
Closed Filter Extendability for \(T_1\) Spaces: Every closed filter in a \(T_1\) topological space can be extended to a maximal closed filter.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M3\) Mathias' model | Mathias proves that the \(FM\) model <a href="/models/Mathias-Pincus-1">\(\cal N4\)</a> can be transformed into a model of \(ZF\), \(\cal M3\) |
| \(\cal M40(\kappa)\) Pincus' Model IV | The ground model \(\cal M\), is a model of \(ZF +\) the class form of \(AC\) |
| \(\cal M45\) Pincus' Model VII | This is the model of <a href="/articles/Pincus-1977a">Pincus [1977a]</a>, Theorem 2.1 \((C)\) |
Code: 3
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