Statement:
There is a function \(f :\omega_1\rightarrow \omega^{\omega}_1\) such that for every \(\alpha\), \(0 < \alpha < \omega_1\), \(f(\alpha )\) is a function from \(\omega\) onto \(\alpha\).
Howard_Rubin_Number: 245
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:
Litman-1976: The monadic theory of \(\omega_1\)
Book references
Note connections:
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 245 A | There is a function \(g : \omega_1\rightarrow \omega^{\omega}_1\) such that for all limit ordinals \(\alpha < \omega_1\), \(g(\alpha)\) is an increasing function from \(\omega\) into \(\alpha\) with the range of \(g\) cofinal in \(\alpha\). |
Litman [1976]
|
| 245 B |
Every closed set \(A\) in \(\omega_1\) which contains only limit ordinals is a derivative (that is,
\(\exists B\subseteq \omega_{1}\) such that |
Litman [1976]
|