On the Degrees of Index Sets
نویسندگان
چکیده
منابع مشابه
On the Degrees of Index Sets
A class of recursively enumerable sets may be classified either as an object in itself — the range of a two-place function in the obvious way — or by means of the corresponding set of indices. The latter approach is not only more precise but also, as we show below, provides an alternative method for solving certain problems on recursively enumerable sets and their degrees of unsolvability. The ...
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In [8] we proved that the index-set corresponding to any recursively enumerable degree a is of the highest isomorphism-type possible for sets belonging to S3(a). From the proof of this result we derived Sacks' theorem [4] that the recursively enumerable degrees are dense. In the present paper we classify three other indexsets associated with any given recursively enumerable degree a, namely the...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1966
ISSN: 0002-9947
DOI: 10.2307/1994481