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I ran into a olympiad question on Practical Computer Knowledge.

For A ⊆ ℕ we have a = degT(A) = {B | B ≡T A} and D = {degT(A) | A ⊆ ℕ}. For (D, ≤) that has A ≤T B iff a ≤ b. Which of the following is false:

  1. (D,≤) is a distributive lattice

  2. (D,≤)‌ is bounded (has minimum and maximum)

  3. (D,≤) is a half disjunctive lattice. (may be I‌ worded this statement poorly, sorry)

  4. he maximum elements of (D,≤) is a degree of Halting Problem .

I think degT means Turing Degree and ≤T‌ means Turing Reduciblity.

Who can give me a hint for these options, we want to check the answer sheet that wrote (1) is correct?

Community
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    I'm voting to close this question as off-topic because it is a computer science question and not a programming question. It may be more suitable at a different [se] site. – Ken White Apr 10 '15 at 16:31
  • I'm voting to close this question as off-topic because it belongs to math.stackexchange.com – schnaader Jun 01 '15 at 06:55
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    https://cs.stackexchange.com/questions/41214/halting-problem-and-turing-degree-and-reduction – David Eisenstat Jun 27 '15 at 14:54
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    I'm voting to close this question as off-topic because this does appear about theoretic computer sciences, not programming. The [version at CS.SE](https://cs.stackexchange.com/q/41214/17342) would be better suited. That has been closed, too, but for being unclear, not for being off topic. So editing there to clarify might help getting that reopened. Or perhaps the answers and comments there are already sufficient. – MvG Sep 07 '16 at 19:40

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