Talk:Computable set

message: Right now, Computable set redirects to recursive set.  Are there any objections if I reverse that redirect? CMummert 23:35, 16 July 2006 (UTC)
thread_title:  Reverse redirect 

message: For anyone keeping this article on their watchlist: there is currently an attempt at merging a number of articles on (non-)recursive/(un)decidable/(un)computable sets/languages/decision problems into a single, thorough article. The experiment currently sits at Recursive languages and sets. Comments are very welcome. Pichpich (talk) 00:42, 21 February 2008 (UTC)
replies: text: Oppose merger A lot of effort has gone into perfecting Recursively enumerable set. I do not want it to be destroyed by merging it into another, inferior article. JRSpriggs (talk) 01:33, 27 May 2008 (UTC)

text: Oppose and remove template  My reasons are quite independent of the current state of the article.  The fact is that r.e. sets can be significantly more complex than recursive ones, and there's quite a lot to say about them. Since this proposal has attracted no support in more than five months, I'm removing the template. --Trovatore (talk) 02:38, 9 August 2008 (UTC)
thread_title:  attempt to merge 

message: Hi. Some time ago the interesting set P^4({}) = P( P( P(P({})))) has been used in the logical connectives article, but was removed. 
Originally this came from Commons user Dohduhdah and his homepage. Where ever he's got this from, he doesn't remember.
In the description of his diagram :File:Set0.gif (hard to read, but equal to my Hasse diagram on the right) he calls this "recursive sets". Does it make sense?
Thanks, Watchduck (talk) 13:17, 12 June 2009 (UTC)
replies: text: I think he is confusing recursive sets with pure sets. JRSpriggs (talk) 21:08, 12 June 2009 (UTC)
replies: text: Possibly, as they are pure for sure. But I should mention, that there is a bijection between these sets and natural numbers. On the right, you see the first sixteen sets between {} = 0 and { {} , {{}}, {{{}}} , {{},{{}}} } = 15. The next set would be {{}} = 16, and so on. Maybe it's helpful to know that, to decide if they are both pure and recursive. Watchduck (talk) 11:01, 13 June 2009 (UTC)
thread_title:  [[Power set]]s of the [[empty set]] 

message: The diagram at the top of the page is misleading: decidable sets are a subset of recursively enumerable sets, but not of undecidable sets.  —Preceding unsigned comment added by 78.131.31.31 (talk) 18:38, 9 November 2009 (UTC)
thread_title:  Diagram Misleading 

message: Because the empty set and the set of natural numbers are recursive sets, and because recursive sets are closed under intersections, unions, and complements, they form a boolean algebra. Computably enumerable sets are closed under intersections and unions but not under complements and thus form a (bounded) distributive lattice. These are fun facts, but I don't know if they are of any use at all (I am by no means an expert in computability theory). If these facts are useful then I suggest that they be added to this article as well the article 'recursively enumerable set', and even if they are totally useless, perhaps they are interesting enough to be included anyway. Let me know what you think. Joel Brennan (talk) 20:50, 16 May 2019 (UTC)
replies: text: Sounds like a good idea to me, if you include a reference. JRSpriggs (talk) 09:09, 17 May 2019 (UTC)
thread_title:  Boolean algebra of recursive sets