Hypothesis: HR 6:
\(UT(\aleph_0,\aleph_0,\aleph_0,\Bbb R)\): The union of a denumerable family of denumerable subsets of \({\Bbb R}\) is denumerable.
Conclusion: HR 249:
If \(T\) is an infinite tree in which every element has exactly 2 immediate successors then \(T\) has an infinite branch.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N35\) Truss' Model IV | The set of atoms, \(A\), is denumerable andeach element of \(A\) is associated with a finite sequence of zeros andones |
Code: 3
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