Hypothesis: HR 42:
Löwenheim-Skolem Theorem: If a countable family of first order sentences is satisfiable in a set \(M\) then it is satisfiable in a countable subset of \(M\). (See Moore, G. [1982], p. 251 for references.
Conclusion: HR 371:
There is an infinite, compact, Hausdorff, extremally disconnected topological space. Morillon [1993].
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M27\) Pincus/Solovay Model I | Let \(\cal M_1\) be a model of \(ZFC + V =L\) |
Code: 3
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