## Journal of Symbolic Logic

### On the Convergence of Query-Bounded Computations and Logical Closure Properties of C.E. Sets

Timothy H. McNicholl

#### Abstract

Call a set A n-correctable if every set Turing reducible to A via a Turing machine that on any input makes at most n queries is Turing reducible to A via a Turing machine that on any input makes at most n-queries and on any input halts no matter what answers are given to its queries. We show that if a c.e. set A is n-correctable for some n $\geq$ 2, then it is n-correctable for all n. We show that this is the optimal such result by constructing a c.e. set that is 1-correctable but not 2-correctable. The former result is obtained by examining the logical closure properties of c.e. sets that are 2-correctable.

#### Article information

Source
J. Symbolic Logic, Volume 66, Issue 4 (2001), 1543-1560.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746611

Mathematical Reviews number (MathSciNet)
MR1877009

Zentralblatt MATH identifier
1002.03036

JSTOR