Post's program and incomplete recursively enumerable sets.
Authors:
- 15 November 1991
- journal article
- Published by National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 88 (22) , 10242-10246
Abstract
A set A of nonnegative integers is recursively enumerable (r.e.) if A can be computably listed. It is shown that there is a first-order property, Q(X), definable in E, the lattice of r.e. sets under inclusion, such that (i) if A is any r.e. set satisfying Q(A) then A is nonrecursive and Turing incomplete and (ii) there exists an r.e. set A satisfying Q(A). This resolves a long open question stemming from Post's program of 1944, and it sheds light on the fundamental problem of the relationship between the algebraic structure of an r.e. set A and the (Turing) degree of information that A encodes.Keywords
This publication has 1 reference indexed in Scilit:
- TWO RECURSIVELY ENUMERABLE SETS OF INCOMPARABLE DEGREES OF UNSOLVABILITY (SOLUTION OF POST'S PROBLEM, 1944)Proceedings of the National Academy of Sciences, 1957