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1 results

  • On the convergence of query-bounded computations and logical closure properties of c.e. sets

  • Timothy H. McNicholl
  • Journal:
    The Journal of Symbolic Logic / Volume 66 / Issue 4 / December 2001
    Published online by Cambridge University Press:
    12 March 2014, pp. 1543-1560
    Print publication:
    December 2001

  • 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 ≥ 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.