Hypothesis: HR 0: \(0 = 0\).
Conclusion: HR 180:
Every Abelian group has a divisible hull. (If \(A\) and \(B\) are groups, \(B\) is a divisible hull of \(A\) means \(B\) is a divisible group, \(A\) is a subgroup of \(B\) and for every non-zero \(b \in B\), \(\exists n \in \omega \) such that \(0\neq nb\in A\).) Fuchs [1970], Theorem 24.4 p 107.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M23\) Hodges' Model | Let \(\cal M\) be a countable transitive model of \(ZFC + V = L\) and let \(\kappa\) be a regular cardinal in \(\cal M\) |
Code: 3
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