User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-5529393-20130627000838

Sorry Ikosarakt1 for not responding earlier.

For rule PB6, it should say \(\alpha > 1\) rather than \(\alpha \ge 1\).

For rule P7, the right hand side of the first equation should have an \(\alpha+1\) rather than an \(\alpha\). Also, you should specify that rule P7 only applies when rule P3 doesn't

Otherwise, those two rulesets look fine. Unfortunately, I don't think the \(\theta\) rules work quite yet. Note that if \(\alpha\) is countable, then \(\alpha + \Omega = \alpha * \Omega = \Omega\), so that messes up rules T8 and T9. Even if you specify that \(\alpha must be an exponential polynomial of \(\Omega\), note that \(\alpha * \Omega\) is always a power of \(\Omega\), so for instance there is no rule that handles \(\Omega^2 * 2\), for instance.