∑5-completeness of index sets arising from the lattice of recursively enumerable sets
نویسندگان
چکیده
منابع مشابه
On the Lattice of Recursively Enumerable Sets
This paper presents some new theorems concerning recursively enumerable (r.e.) sets. The aim of the paper is to advance the search for a decision procedure for the elementary theory of r.e. sets. More precisely, an effective method is sought for deciding whether or not an arbitrary sentence formulated in the lower predicate calculus with sole relative symbol £ is true of the r.e. sets. The main...
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For given sets A, B, and Z of natural numbers where the members of Z are z0, z1, . . . in ascending order, one says that A is selected from B by Z if A(i) = B(zi) for all i. Furthermore, say that A is selected from B if A is selected from B by some recursively enumerable set, and that A is selected from B in n steps iff there are sets E0, E1, . . . , En such that E0 = A, En = B, and Ei is selec...
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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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We study here the degree-theoretic structure of set-theoretical splittings of recursively enumerable r.e. sets into diierences of r.e. sets. As a corollary we deduce that the ordering of wttdegrees of unsolvability of diierences of r.e. sets is not a distributive semilattice and is not elementarily equivalent to the ordering of r.e. wttdegrees of unsolvability.
متن کاملUniversal Recursively Enumerable Sets of Strings
The present work clarifies the relation between domains of universal machines and r.e. prefix-free supersets of such sets. One such characterisation can be obtained in terms of the spectrum function sW (n) mapping n to the number of all strings of length n in the set W . An r.e. prefix-free set W is the superset of the domain of a universal machine iff there are two constants c, d such that sW ...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1996
ISSN: 0168-0072
DOI: 10.1016/0168-0072(95)00055-0