Hypothesis: HR 3: \(2m = m\): For all infinite cardinals \(m\), \(2m = m\).
Conclusion: HR 88:
\(C(\infty ,2)\): Every family of pairs has a choice function.
List of models where hypothesis is true and the conclusion is false:
| Name | Statement |
|---|---|
| \(\cal N9\) Halpern/Howard Model | \(A\) is a set of atoms with the structureof the set \( \{s : s:\omega\longrightarrow\omega \wedge (\exists n)(\forall j > n)(s_j = 0)\}\) |
Code: 5
Comments: