I was searching for interesting and easy to state open problems in computability (understandable by undergraduate students taking their first course in computability) to give examples of open problems (and obviously I want the students to be able to understand the problem without needing too much new definitions and also be interesting to them).
I found this list but the problems in it seem too complicated for undergraduates and will need spending considerable time giving definitions before stating the problem. The only problem I have found so far is
Is Diophantine problem over rational numbers decidable?
Do you know any other interesting and easy to state open problem in computability theory?