User blog comment:King2218/FGH Things/@comment-25418284-20140305080757/@comment-25418284-20140306045139

The problem I'm having is this: let's try \(f_{\varepsilon_0}(\omega 2)\). Naively extending my definition for \(f_\alpha(\omega)\) yields \(\sup\{f_{\varepsilon_0[\omega]}(\omega 2), f_{\varepsilon_0[\omega + 1]}(\omega 2), f_{\varepsilon_0[\omega + 2]}(\omega 2), \ldots\}\). So...what is \(\varepsilon_0[\omega + 1]\)?