User blog comment:KthulhuHimself/Ordinal Arithmetic Notation (OAN)/@comment-35470197-20191112141154/@comment-35470197-20191117093108

> If you look at the definition, you'll see that it is indeed encoded in arithmetic.

No. It is not literally encoded in arithmetic, because you actually used ordinals and set theoretic operators on ordinals such as limits. Therefore it is not computable in the sense that it has not been encoded into a numerical notation equipped with operations whose computations are given by specific algorithm you have written.