Hypothesis: HR 305:
There are \(2^{\aleph_0}\) Vitali equivalence classes. (Vitali equivalence classes are equivalence classes of the real numbers under the relation \(x\equiv y\leftrightarrow(\exists q\in{\Bbb Q})(x-y=q)\).). \ac{Kanovei} \cite{1991}.
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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