I want to start a project to explicitly generate the Gödel sentence on the incompleteness theorem (Rosser version, Robison Arithmetic, with Gödel numbers in it -- the full thing). I read some proofs of it, Smullyan on its Incompleteness Theorem book, and Boolos Jeffrey Burgess proof. I think the problem to generate it with the help of a average modern computer is the beta function. Beta functions based on the Chinese theorem seems to be an impossible choice. Now, I think Smullyan beta function seems feasible (p.45, the way I see it, it seems to be based on a kind of ASCII-string code). So here are the questions:
- What is the better approach to construct this beta function? (do you have any reference? etc...)
- Is the Smullyan way feasible?
- Do you have some tips?
- Do you think Python is good for it?
Ok, I know this has a lot of details, and it is required some programming skills. I know some Python, C, I am aiming to learn more, so this is a long term project. I was looking more tips just to not take the wrong direction.
Ps: I noticed there is this aswer, but I was more looking for some advice rather than the sentence.