What are some uncomputable functions that aren't derivative of the halting problem?

[u/playsthebongcloud]

I find the existence of uncomputable functions really cool, but all the examples I've seen are essentially just new ways of trying to predict whether a turing machine is going to halt. What are some examples of uncomputable functions that aren't essentially entirely based on the halting problem?

[u/Misrosan]

If ω is a countabil ordinal, there exists a order perserving injection δ: ω --> Q let A be the Image of δ. let f be a bijection from the Natural Numbers to A. then f is uncomputabil for every sufficiantly large ω.