On Wed, Jun 18, 2008 at 1:58 AM, Abram Demski <[EMAIL PROTECTED]> wrote: > Vladimir Nesov, > > Then do you agree with my hypothetical extremist version of Mike? > > (Aside: For the example we are talking about, it is totally necessary > to stick the undecidable cases in F rather than T: if a Turing machine > halts, then it is possible to prove that it halts (simply by running > it for long enough). So if a Turing machine is one of those whose > halting is formally undecidable, then it must not halt, because if it > did then a proof of its halting would exist.) >
If T* is enumerable set of halting machines, F* is enumerable (by our machine) subset of never-halting machines, and X is set of remaining machines, the situation is symmetric. If you dump X into T*, you destroy its property to be enumerable, but likewise with F*. -- Vladimir Nesov [EMAIL PROTECTED] ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=106510220-47b225 Powered by Listbox: http://www.listbox.com
