Good thing Computability Beyond Church-Turing via Choice Sequences[1] exists.
[1] Mark Bickford, Liron Cohen, Robert L. Constable, and Vincent Rahli. 2018. Computability Beyond Church-Turing via Choice Sequences. In Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS '18). Association for Computing Machinery, New York, NY, USA, 245–254. https://doi.org/10.1145/3209108.3209200
[1] Mark Bickford, Liron Cohen, Robert L. Constable, and Vincent Rahli. 2018. Computability Beyond Church-Turing via Choice Sequences. In Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS '18). Association for Computing Machinery, New York, NY, USA, 245–254. https://doi.org/10.1145/3209108.3209200