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I want to bound some functions using the fast-growing hierarchy, but for accounting reasons it looks like it's going to be easier to deal with a modified hierarchy that grows at "$1/\omega$-th" the rate: my first guess at the hierarchy I want is

  • $f_0(x)=x+1$
  • $f_{\lambda}(x)=f_{\lambda[x]}(x)$
  • $f_{\lambda+n}(x)=f_\lambda^n(x)$

Has this, or perhaps some more carefully thought out version, appeared in the literature?

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  • $\begingroup$ your second and third rules are only for limit ordinals? $\endgroup$
    – Will Sawin
    Commented Aug 17, 2016 at 0:25
  • $\begingroup$ @WillSawin: Yes. (Though I'm not wedded to these precise rules, which seem very slightly wonky in ways I'm having trouble placing; one of the reasons I'm asking is that someone may have gotten them right and saved me the trouble.) $\endgroup$
    – Henry Towsner
    Commented Aug 17, 2016 at 1:16

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