Statement:
Antichain Principle: Every partially ordered set has a maximal antichain. Jech [1973b], p 133.
Howard_Rubin_Number: 89
Parameter(s): This form does not depend on parameters
This form's transferability is: Not Transferable
This form's negation transferability is: Negation Transferable
Article Citations:
Kurepa-1953: Uber das Auswahlaxiom
Book references
The Axiom of Choice, Jech, T., 1973b
Note connections:
Note 39
In this note the results
of Harper/Rubin [1976] are summarized.
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 89 A | If \(\forall y\in X\), \(y = \langle u,R\rangle\) where \(R\) is a partial order on \(u\) then there is a function \(f\) on \(X\) such that \(\forall\langle u,R\rangle\in X\), \(f(\langle u,R\rangle)\) is a maximal antichain in \(u\). |
Felgner [1969]
Harper-Rubin-1976
|