User blog comment:Testitemqlstudop/On mapping positive integers to ordinals/@comment-43798125-20191027101113/@comment-35470197-20191027141158

I also have a similar surjective map onto e_0 using the 2-adic encoding here, in which two natural numbers correspond to the same ordinal if and only if its ratio is a power of 2. (The reason why I made it non-injective is because I wanted to create a 1-ary large function without any multivariable recursion.)

There are several methods to extend it. For example, I created a 10-adic encoding, which essentially gives a surjective map onto PTO(Π11-CA0) here. It is also a 1-ary large function without any multivariable recursion.