Σ5-completeness of index sets arising from the recursively enumerable Turing degrees
نویسندگان
چکیده
منابع مشابه
Generating Sets for the Recursively Enumerable Turing Degrees
One of the recurrent themes in the area of the recursively enumerable (r.e.) degrees has been the study of the meet operator. While, trivially, the partial ordering of the r.e. degrees is an upper semi-lattice, i.e., the join ∗Lempp was partially supported by NSF grant DMS-0140120 and a Mercator Guest Professorship of the Deutsche Forschungsgemeinschaft. †Slaman was partially supported by the A...
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TABLE OF CONTENTS Introduction Chapter I. The relation of the structure of an r.e. set to its degree. 1. Post's program and simple sets. 2. Dominating functions and quotient lattices. 3. Maximal sets and high degrees. 4. Low degrees, atomless sets, and invariant degree classes. 5. Incompleteness and completeness for noninvariant properties. Chapter II. The structure, automorphisms, and elementa...
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Decision problems were the motivating force in the search for a formal definition of algorithm that constituted the beginnings of recursion (computability) theory. In the abstract, given a set A the decision problem for A consist of finding an algorithm which, given input n, decides whether or not n is in A. The classic decision problem for logic is whether a particular sentence is a theorem of...
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We embed the upper semilattice of r.e. Turing degrees into a slightly larger structure which is better behaved and more foundationally relevant. For P,Q ⊆ 2, we say P is Muchnik reducible to Q if for all Y ∈ Q there exists X ∈ P such that X is Turing reducible to Y . We let Pw denote the lattice of Muchnik degrees of nonempty Π1 subsets of 2. Pw is a countable distributive lattice with 0 and 1....
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The biinterpretability conjecture for the r.e. degrees asks whether, for each sufficiently large k, the Σk relations on the r.e. degrees are uniformly definable from parameters. We solve a weaker version: for each k ≥ 7, the Σk relations bounded from below by a nonzero degree are uniformly definable. As applications, we show that Low1 is parameter definable, and we provide a new example of a ∅–...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1996
ISSN: 0168-0072
DOI: 10.1016/0168-0072(95)00054-2