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Results tagged with computability-theory
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user 65995
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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Will this Turing machine find a proof of its halting?
Build a second machine $N$. $N$ searches for a proof in ZFC of, "if $N$ halts then $M$ halts". If it finds one, it halts.
ZFC can argue as follows. "Suppose $N$ halts. Then it found a proof that if $N …
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