Cohen \(\cal M7(n)\): Generalization of \(\cal M7\) | Back to this models page
Description: Model \(\cal M7\) can be generalized to \(n\) denumerable sets for \(1 \le n \in\omega\), then the Axiom of Choice for a denumerable number of \(n\) element sets, \(C(\aleph_0,n)\), is false for \(1 \le n \le \omega\)
When the book was first being written, only the following form classes were known to be true in this model:
| Form Howard-Rubin Number | Statement |
|---|---|
| 0 | \(0 = 0\). |
When the book was first being written, only the following form classes were known to be false in this model:
| Form Howard-Rubin Number | Statement |
|---|---|
| 47-n | If \(n\in\omega-\{0,1\}\), \(C(WO,n)\): Every well ordered collection of \(n\)-element sets has a choice function. |
| 91 | \(PW\): The power set of a well ordered set can be well ordered. |
Historical background:
Therefore, \(C(WO,n)\) (47(\(n\))) is also false for\(1