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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.
12
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Succinctly naming big numbers: ZFC versus Busy-Beaver
It seems that the philosophical position you're taking for granted is close to the position called "predicativism" advocated by mathematicians such as Poincarè and Weyl, and whose boundaries have been …