We have the following indirect implication of form equivalence classes:
315
\(\Rightarrow\)
315
given by the following sequence of implications, with a reference to its direct proof:
| Implication |
Reference |
|
315
\(\Rightarrow\)
315
|
|
Here are the links and statements of the form equivalence classes referenced above:
| Howard-Rubin Number |
Statement |
| 315: |
\(\Omega = \omega_1\), where
\(\Omega = \{\alpha\in\hbox{ On}: (\forall\beta\le\alpha)(\beta=0 \vee (\exists\gamma)(\beta=\gamma+1) \vee\)
there is a sequence \(\langle\gamma_n: n\in\omega\rangle\) such that for each \(n\),
\(\gamma_n<\beta\hbox{ and } \beta=\bigcup_{n<\omega}\gamma_n.)\} \)
|
| 315: |
\(\Omega = \omega_1\), where
\(\Omega = \{\alpha\in\hbox{ On}: (\forall\beta\le\alpha)(\beta=0 \vee (\exists\gamma)(\beta=\gamma+1) \vee\)
there is a sequence \(\langle\gamma_n: n\in\omega\rangle\) such that for each \(n\),
\(\gamma_n<\beta\hbox{ and } \beta=\bigcup_{n<\omega}\gamma_n.)\} \)
|
Comment: