Computability with two-place oracle (Q1920828)

A kind of Turing machine which can use partial functions as an oracle is discussed. For such a machine with a partial oracle \(F\), the function of the halting problem \(g_F(x)\) is defined as 0 or 1 if the machine halts or works endlessly, respectively, and for any question asked by the machine, the oracle gives the answer. If the oracle does not give an answer to some question (because the oracle is partial), \(g_F(x)\) is undefined. The main result of this paper indicates that there are partial oracles \(F\) for which the function \(g_F\) is \(F\)-computable.