Complementing below recursively enumerable degrees
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...
متن کاملRecursively Enumerable Sets and Degrees
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...
متن کاملParameter definability in the recursively enumerable degrees
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 ∅–...
متن کاملExtensions of Embeddings below Computably Enumerable Degrees
Toward establishing the decidability of the two quantifier theory of the ∆ 2 Turing degrees with join, we study extensions of embeddings of upper-semi-lattices into the initial segments of Turing degrees determined by computably enumerable sets, in particular the degree of the halting set 0. We obtain a good deal of sufficient and necessary conditions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1987
ISSN: 0168-0072
DOI: 10.1016/0168-0072(87)90039-x