Linked from

The 32 pages that link to Halting problem, each with the reason it gives.

• Turing machineBroader topic: Turing machines make the impossibility of a general halting test precise.

• Alan TuringBroader topic: Turing proved that no algorithm can solve it for every possible program and input.

• Computability theoryBroader topic: It is the canonical example of a well-defined problem that no algorithm decides.

• Decision problemBroader topic: It is a canonical decision problem proved impossible to solve in full generality.

• DecidabilityBroader topic: Its undecidability shows that no general algorithm decides every computation's termination.

• DiagonalizationBroader topic: Its undecidability proof builds a program that contradicts any proposed universal decider.

• Undecidable problemBroader topic: Turing proved that no algorithm decides this particular problem for every program and input.

• Arithmetical hierarchyBroader topic: Its set of halting instances is Σ⁰₁-complete.

• Computably enumerable setBroader topic: Its positive instances form a computably enumerable set, but its negative instances do not.

• Post's theoremBroader topic: The first Turing jump is the halting problem, matching the first noncomputable level.

• Theory of computationBroader topic: Its undecidability demonstrates that some well-defined computational questions have no general algorithm.

• Turing's proofBroader topic: Turing’s construction proves that no algorithm solves this problem for all machines and inputs.