User blog comment:Ubersketch/What are some ways to map a well-order to the natural numbers without using a Godel coding/@comment-39541634-20190909210146/@comment-39541634-20190910193511

Something I just realized:

What exactly do you mean by "without Godel coding"? Do you require this because you want simple examples that not require an understanding of proof theory, or because you consider Godel coding "cheating"?

I'm asking, because as P-bot mentioned, unless the ordinal in question is very small, an easy-to-follow mapping would have to be a thinly veiled Godel code. So if it is simplicity that you seek, you're going to love these examples. But if you consider any form of Godel coding to be a cheat, then they are going to disappoint you and I'll have to wreck my brains and think of something else.

So which is it? I thought it would be a good idea to check, before I write a 5-page long comment that misunderstands what you asked for...