Statement:
Weak Partition Principle: For all sets \(x\) and \(y\), if \(x\precsim^* y\), then it is not the case that \(y\prec x\).
Howard_Rubin_Number: 100
Parameter(s): This form does not depend on parameters
This form's transferability is: Unknown
This form's negation transferability is: Negation Transferable
Article Citations:
Lindenbaum-Tarski-1926: Communication sur les recherches de la th'eorie des ensembles
Book references
Note connections:
Note 69
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 100 A | For every set \(A\) and function \(f\) it is false that \(A \prec f''A\). G. Moore [1982], p. 327. |
Book: Zermelo's Axiom of Choice |
| 100 B | For all sets \(x\) and \(y\), if \(x\precsim^* y\) and \(y\precsim x\), then \(x\approx y\). |
Higasikawa [1995]
Note [69] |