Statement:
Cardinal Representatives: For every set \(A\) there is a function \(c\) with domain \({\cal P}(A)\) such that for all \(x, y\in {\cal P}(A)\), (i) \(c(x) = c(y) \leftrightarrow x\approx y\) and (ii) \(c(x)\approx x\). Jech [1973b] p 154.
Howard_Rubin_Number: 97
Parameter(s): This form does not depend on parameters
This form's transferability is: Unknown
This form's negation transferability is: Unknown
Article Citations:
Book references
The Axiom of Choice, Jech, T., 1973b
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 97 A | For every set \(\{X_i: i\in I\}\) of local cardinal numbers, there is a set \(\{x_i: i\in I\}\) of sets such that for each \(i\in I\) there exists a \(y_i\in X_i\) such that \(x_i\approx y_i\). (\(X\) is a local cardinal number if for all \(x, y\in X\), \(x\approx y\).) |
Higasikawa [1995]
|