There are various verticals. But of all these verticals there are roots. Sort of like how Set theory and Category theory make up the fundamental basis of all m

There are various verticals. But of all these verticals there are roots. Sort of like how Set theory and Category theory make up the fundamental basis of all math, the fundamentals of computer science are encoded within your first example: >For instance, there is a whole subset devoted to turing machines, the halting problem, finite state machines, provability, incompleteness, the set of all sets, diagonalization proofs etc