The recursively enumerable α-degrees are dense
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This article is published in Annals of Mathematical Logic.The article was published on 1976-01-01 and is currently open access. It has received 122 citations till now. The article focuses on the topics: Recursively enumerable language.read more
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Book
Algorithmic Randomness and Complexity
TL;DR: This chapter discusses Randomness-Theoretic Weakness, Omega as an Operator, Complexity of C.E. Sets, and other Notions of Effective Randomness.
Book
Higher recursion theory
TL;DR: In this article, hyperarithmetic theory is developed at length and used to lift classical recursion theory from integers to recursive ordinals (metarecursion) and two further liftings are then made, first ordinals and then sets (E-recursion).
Journal ArticleDOI
Automorphisms of the lattice of recursively enumerable sets
TL;DR: In this article, it was shown that for any two maximal sets A and B, there exists a group of automorphisms (Aut
Book ChapterDOI
Degrees of Unsolvability
Klaus Ambos-Spies,Peter A. Fejer +1 more
TL;DR: The notion of degree of unsolvability was introduced by Post in [Post, 1944] and has been used extensively in computability theory as mentioned in this paper, where a set A is computable relative to a set B, and B is Turing reducible to A.
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Degrees of unsolvability of continuous functions
TL;DR: It is shown that the Turing degrees are not sufficient to measure the complexity of continuous functions on [0, 1], and the continuous degrees are introduced and proved to be a proper extension of the Turing degree and a proper substructure of the enumeration degrees.
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On degrees of unsolvability
TL;DR: In this article, it was shown that there are degrees between 0 and 0' which are not recursively enumerable and the existence of such degrees follows from the following theorem, which may be roughly stated for d = 0 as: if a > 0', then the degrees < a cannot be enumerated by a function of degree < a.