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computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.
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Physics and Church–Turing Thesis
Robin Gandy once wrote a paper listing axioms about physics that implied the Church-Turing thesis. I'm sure you could find it by searching for all articles written by him.
Also, Frank Tipler once …