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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.

6 votes

Can We Decide Whether Small Computer Programs Halt?

On the flip side, one can write a program that does the Collatz sequence or walks through an enumeration of natural number vectors to see if it has a solution to some Diophantine equation whose solubi …
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