Statement:
Suppose \(k\in\omega\). If \(f\) is a partial map from \(k\times Y\) onto \(k\times X\) (that is, the domain is a subset of \(k\times Y\)), then there are partitions \(X = \bigcup_{i \le k} X_{i}\) and \(Y = \bigcup_{i \le k} Y_{i}\) of \(X\) and \(Y\) such that \(f\) maps \(\bigcup_{i \le k} (\{i\} \times Y_{i})\) onto \(\bigcup^{}_{i \le k} (\{i\} \times X_{i})\).
Howard_Rubin_Number: 138-k
Parameter(s): This form depends on the following parameter(s): \(k\),
This form's transferability is: Unknown
This form's negation transferability is: Negation Transferable
Article Citations:
Truss-1984: Cancellation laws for surjective cardinals
Book references
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 138 A-k | For all standard \(X\) and \(Y\), Form 138(\(k\)) holds. This is equivalent to Form 138(\(k\)) in \(ZF^{0}\). |
Truss [1984]
|