Turing Incompleteness Theorem

The TuringIncompletenessTheorem is a theorem that reads "There are no nontrivial questions about the result of a Turing machine that can be answered by a Turing machine for all Turing machines."

See HaltingProblem for why this is true.

It's better known as RicesTheorem.

[Ah yes. From the other size of The ChurchTuringThesis.]

There are several ways to prove it, of course, but the one I'm most familiar is to reduce it to the HaltingProblem. How does that make it the "other size[side?] of the ChurchTuringThesis"?

[Because RicesTheorem is based from lambda calculus. I believe the fact of identical theorems with both mechanisms was instrumental in proving the ChurchTuringThesis.]

It's not. It's based on TMs. Now one can also prove it based on LambdaCalculus, KleenesHierarchy?, and some other things, but it's usually done in terms of TMs.


EditText of this page (last edited July 14, 2013) or FindPage with title or text search