Hypothesis: HR 263:
\(H(AS\&C,P)\): Every every relation \((X,R)\) which is antisymmetric and connected contains a \(\subseteq\)-maximal partially ordered subset.
Conclusion: HR 64:
\(E(I,Ia)\) There are no amorphous sets. (Equivalently, every infinite set is the union of two disjoint infinite sets.)
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
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