Forum:Buchholz's FS system

For a while I thought that the Wainer hierarchy (\(\mu = \varepsilon_0 + 1\)) was the largest fundamental sequence system known to be increasing in FGH -- that is, for all \(\alpha < \beta < \mu\), \(f_\alpha\) is eventually dominated by \(f_\beta\). Wojowu pointed out to me that, in the paper introducing his hydra, Buchholz created a fundamental sequence system with \(\mu = \text{TFB}\) and proved that it is increasing (lemma 3.6d).

A few questions remain before this hierarchy is useful to us. For example, is it an extension of the Wainer hierarchy? -- vel! 18:35, August 17, 2015 (UTC)