Talk:Post's theorem

Comments 2006-10-25
The article has been sitting in a half-finished state for a while. I expanded it and set it up for further improvement. CMummert 13:42, 25 October 2006 (UTC)
 * This article needs to be at an undergraduate level at the highest
 * More references, especially at the undergrad level, are needed
 * The notation should be kept as simple as possible (but not more simple than that).
 * I think that a proof would be nice, and the proof is elementary anyway.
 * More corollaries would be good.

Quantifier Blocks
I believe the 'alternative' definition I added using quantifier blocks and bounded quantifiers should probably be the primary definition. However, I don't remember and need to get back to working on my thesis.Logicnazi (talk) 02:46, 24 November 2007 (UTC)

Definition of $$\Sigma^{0}_m$$
The definition of $$\Sigma^{0}_m$$ differs from the traditional one for $$m=0$$ since it would not allow bounded quantifiers. Since Post theorem doesn't say anything about $$\Sigma^0_0$$ relation this doesn't affect the theorem, but it seems misleading. Catrincm (talk) 13:34, 30 September 2014 (UTC)

T halts on input n at time n1 at most if and only if $$\varphi(n,n_1)$$ is satisfied
What does it mean: "at most if and only if"? Is it equivalence or one-direction consequence?

Eugepros (talk) 10:08, 6 October 2018 (UTC)


 * I think they mean to say that $$\varphi(n,n_1)$$ is true if and only if $$T$$ halts at or prior to time $$n_1$$. Related to that, the assertion that $$\varphi$$ can be a $$\Delta_0$$ formula (only having bounded quantifiers) is almost certainly incorrect, or else it needs a citation. I've never seen any formalization of turing machines where the halting time function is $$\Delta_0$$. Obviously $$\varphi$$ is $$\Delta_1$$, which is sufficient for Post's theorem, and it's even primitive recursive, but the idea that it could be $$\Delta_0$$ seems implausible. Jade Vanadium (talk) 20:13, 8 July 2024 (UTC)