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Not using anything other than the definition of SD and D

I know if A is SD, then there exists a TM M such that A = L(M), and A can be enumerated, and if A is decidable, then everything in A can be enumerated in some order.

How do I set up the diagonal matrix?

user48594
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  • See the first part of http://cs.stackexchange.com/a/11289/157 (link corrected) – Ran G. Apr 29 '16 at 02:25
  • @RanG. The first part is not good enough, since we want the language to be semidecidable. The usual trick is to show that some specific semidecidable language (say the halting problem) is decidable. The question is whether you could carry out the argument without knowing in advance about the halting problem. – Yuval Filmus Apr 29 '16 at 10:09
  • @YuvalFilmus we construct there a co-semi decidable language, whose complement is semi-decidable. It fully answers the above question. – Ran G. Apr 29 '16 at 13:33
  • @RanG. I stand corrected. – Yuval Filmus Apr 29 '16 at 13:36

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