  There are numbers k and s and a URM program A(n,m) satisfying the following
conditions.
  1. If A(n,m) halts, then Cn(m) diverges. 2. For all n, C_k(n) = A(n,n) and
C_s(n) = C_k(s). 3. A(k,s) halts and for all n, A(s,n) diverges.
  Here C_n(_) is a program with index n in some exhaustive enumeration of all
possible programs.
  This has implications for solving the liar paradox and for generalization of
G\"odel incompleteness theorem to formal systems other than PA.
