Recursively enumerable sets and degrees
- R. Soare
- Mathematics
- 1 March 1987
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…
Π⁰₁ classes and degrees of theories
- C. Jockusch, R. Soare
- Mathematics
- 1 November 1972
Recursively enumerable sets and degrees - a study of computable functions and computability generated sets
- R. Soare
- Computer SciencePerspectives 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.
Computability and Recursion
- R. Soare
- Computer ScienceBulletin of Symbolic Logic
- 1 September 1996
After a careful historical and conceptual analysis of computability and recursion, several recommendations are made about preserving the intensional differences between the concepts of “computability” and “recursion.”
An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees
- K. Ambos-Spies, C. Jockusch, R. Shore, R. Soare
- Mathematics
- 1984
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
Automorphisms of the lattice of recursively enumerable sets. Part II: Low sets
- R. Soare
- MathematicsAnnals of Mathematical Logic
- 1 June 1982
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 equivalence…
The d.r.e. Degrees are Not Dense
- S. Cooper, L. Harrington, A. Lachlan, S. Lempp, R. Soare
- Mathematics, PhysicsAnnals of Pure and Applied Logic
- 20 December 1991
Post's program and incomplete recursively enumerable sets.
- L. Harrington, R. Soare
- Computer ScienceProceedings 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.
Degrees of members of Π10 classes
- C. Jockusch, R. Soare
- Mathematics
- 1 March 1972
The infinite injury priority method
- R. Soare
- MathematicsJournal of Symbolic Logic (JSL)
- 1 June 1976
The purpose of this paper is to reduce the Sacks method to two easily understood lemmas whose proofs are very similar to the finite injury case, and proves the Thickness Lemma of Shoenfield and the Yates Index Set Theorem.
...
...