Hypothesis: HR 191:
\(SVC\): There is a set \(S\) such that for every set \(a\), there is an ordinal \(\alpha\) and a function from \(S\times\alpha\) onto \(a\).
Conclusion: HR 210:
The commutator subgroup of a free group is free.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N30\) Läuchli's Model III | The set \(A\) is denumerable; \(\cal G\) isthe group generated by the set of transpositions on \(A\); and \(S\) is theset of all finite subsets of \(A\) |
Code: 5
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