User blog comment:Moooosey/Simple psi-- a fairly simple ocf/@comment-43798125-20191105221608/@comment-39541634-20191107005620

It's nowhere near PTO(KPM).

The strength of a properly-constructed OCF can usually be estimated by the number of independent collapse functions in it.

Your current system has two such functions. Stronger systems would have 3 or 4 or even an infinite number of them.

Even stronger systems would have a mechanism that generates collapse functions on the fly: one collapse function for every countable ordinal you've already generated.

This last trick will get you to an ordinal commonly notated as ψ(ΩΩ). This is still vastly smaller then PTO(KPM), which requires the use of something called a Mahlo cardinal (or a concept of equivalent power) to attain.

You're not yet ready to yield that power. Heck, niether am I. Mahlos are scary. There are, like, three people on this entire wiki that truly understand how these work.