 These observations in turn license the use of the expression computable in \(A\) to describe both a function \(f(\vec{x})\) which is \(A\)-partial recursive and total and also a set \(B\) such that \(\chi_B(x)\) is computable in \(A\). We also use the expression computably enumerable (c.e.) in \(A\) to describe a set \(B\) which is the range of an \(A\)-partial recursive function and the notation \(W^A_e\) to denote the domain of \(\phi^{A}_e(x)\). It is then straightforward to see that many of our prior proofs about non-computability also carry over to the relativized setting—e.g., \(K^A = \{i : \phi^{A}_i(i)\darrow\}\) is an example of a set which is computably enumerable in \(A\) but not computable in \(A\).