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Recursively 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 setsExpand
Computability and recursion
  • R. Soare
  • Computer Science
  • Bull. Symb. Log.
  • 1 September 1996
We consider the informal concept of “computability” or “effective calculability” and two of the formalisms commonly used to define it, “( Turing ) computability ” and “( general ) recursiveness ”. WeExpand
Recursively enumerable sets and degrees - a study of computable functions and computability generated sets
  • R. Soare
  • Computer Science
  • Perspectives in mathematical logic
  • 1 April 1987
The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be. Expand
Automorphisms of the lattice of recursively enumerable sets
Let S denote the lattice of recursively enumerable (r.e.) sets under inclusion, and let #* denote the quotient lattice of S modulo the ideal 3F of finite sets. For A e ê let A* denote the equivalenceExpand
An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees
On donne une decomposition definissable du semi-treillis superieur des degres recursivement enumerables R comme l'union disjointe d'un ideal M et un filtre fort NC
Post's program and incomplete recursively enumerable sets.
  • L. Harrington, R. Soare
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences…
  • 15 November 1991
It is shown that there is a first-order property, Q(X), definable in E, the lattice of r.e. sets under inclusion, which resolves a long open question stemming from Post's program of 1944, and sheds light on the fundamental problem of the relationship between the algebraic structure of an r. Expand
The d.r.e. Degrees are Not Dense
An easy modification yields the nondensity of the n -r.r.e. degrees and of the ω-r. e. degrees of the maximal incomplete d.R.r-e. degree, establishing the nonddensity of the partial order of the d.r .e.degree. Expand