The closed timelike curve computer, and the nested closed timelike curve computer is an interesting intuitive model (for some people) of how the Turing jump and to a lesser extent how an oracle machine works, where the base case is exactly like the familiar computers we know, which can’t solve their own halting problem, but then we add a new closed time-like curve loop and it’s now able to solve the halting problem for ordinary computers, but can’t solve it’s own halting problem, so adds a new time loop to solve it, and so on.
(Of course, you could always define the Turing Jump formally without any problem, without using any concrete model of computation, and you’d eventually transition into formal explanations, similar to how you could define the computable functions on a wide, but not all range of models of computation, but it’s still nice that you can represent the Turing jump with a concrete physical model of computation)
The closed timelike curve computer, and the nested closed timelike curve computer is an interesting intuitive model (for some people) of how the Turing jump and to a lesser extent how an oracle machine works, where the base case is exactly like the familiar computers we know, which can’t solve their own halting problem, but then we add a new closed time-like curve loop and it’s now able to solve the halting problem for ordinary computers, but can’t solve it’s own halting problem, so adds a new time loop to solve it, and so on.
(Of course, you could always define the Turing Jump formally without any problem, without using any concrete model of computation, and you’d eventually transition into formal explanations, similar to how you could define the computable functions on a wide, but not all range of models of computation, but it’s still nice that you can represent the Turing jump with a concrete physical model of computation)
The papers are below:
https://arxiv.org/abs/1609.05507
https://studenttheses.uu.nl/handle/20.500.12932/45273