Hypothesis: HR 295:
DO: Every infinite set has a dense linear ordering.
Conclusion: HR 296:
Part-\(\infty\): Every infinite set is the disjoint union of infinitely many infinite sets.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N48\) Pincus' Model XI | \(\cal A=(A,<,C_0,C_1,\dots)\) is called an<em>ordered colored set</em> (OC set) if \(<\) is a linear ordering on \(A\)and the \(C_i\), for \(i\in\omega\) are subsets of \(A\) such that for each\(a\in A\) there is exactly one \(n\in\omega\) such that \(a\in C_n\) |
Code: 3
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