| 31. | The set of all provable sentences in an effective axiomatic system is always a recursively enumerable set.
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| 32. | As intermediate results, Post defined natural types of recursively enumerable sets like the hypersimple and hyperhypersimple sets.
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| 33. | From the A3000 design onwards, it was deemed desirable for all enumerable hardware expansions to use Autoconfig.
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| 34. | Every recursively enumerable ( or even hyperarithmetic ) nonempty subset of this total ordering has a least element.
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| 35. | :A language is recursively enumerable if there is a Turing machine that can generate all its strings.
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| 36. | They built a computably enumerable set that is low for Martin-L�f-randomness but not computable.
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| 37. | Equivalently, a set is recursively enumerable if and only if it is the range of some computable function.
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| 38. | The recursively enumerable sets, although not decidable in general, have been studied in detail in recursion theory.
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| 39. | The study of arbitrary ( not necessarily recursively enumerable ) Turing degrees involves the study of the Turing jump.
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| 40. | This is not difficult; WKL 0 implies the existence of separating sets for effectively inseparable recursively enumerable sets.
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