Hypothesis: HR 250:
\((\forall n\in\omega-\{0,1\})(C(WO,n))\): For every natural number \(n\ge 2\), every well ordered family of \(n\) element sets has a choice function.
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
Comments: