Degrees of unsolvability complementary between recursively enumerable degrees, Part 1
نویسندگان
چکیده
منابع مشابه
The Recursively Enumerable Degrees
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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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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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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The extension of embeddings problem for the recursively enumer-able degrees R = (R; <; 0;0 0) asks for given nite partially ordered sets P Q with least and greatest elements, whether every embedding of P into R can be extended to an embedding of Q into R. Many of the landmark theorems giving an algebraic insight into R assert either extension or nonextension of embeddings. We extend, strengthen...
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1972
ISSN: 0003-4843
DOI: 10.1016/0003-4843(72)90011-3