I understand that the subset $\Phi'$ of $\Phi$ is cofinal by looking at Wikipedia
https://en.wikipedia.org/wiki/Cofinal_(mathematics)
Would anybody explain what the cofinal sequence $(Y_n)$ means?
2025-01-12 23:37:47.1736725067
what is a cofinal sequence?
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It means that the range of the sequence ($Y_n$), i.e. {$Y_n$}, is a cofinal subset of $\Phi$.
In other words, the set {$Y_n$} is a special cofinal subset of $\Phi$: It is indexed by the natural numbers. Moreover, the subset requirements $Y_1$ $\subset$ $Y_2$ $\subset$ ... restrict how the indexes are assigned.