Hypothesis: HR 40:
\(C(WO,\infty)\): Every well orderable set of non-empty sets has a choice function. Moore, G. [1982], p 325.
Conclusion: HR 274:
There is a cardinal number \(x\) and an \(n\in\omega\) such that \(\neg(x\) adj\(^n\, x^2)\). (The expression ``\(x\) adj\(^n\, ya\)" means there are cardinals \(z_0,\ldots, z_n\) such that \(z_0 = x\) and \(z_n = y\) and for all \(i,\ 0\le i < n,\ z_i< z_{i+1}\) and if \(z_i < z\le z_{i+1}\), then \(z = z_{i+1}.)\) (Compare with [0 A]).
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal M2\) Feferman's model | Add a denumerable number of generic reals to the base model, but do not collect them |
Code: 3
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