\(\Delta_ 1\)-definability (Q1377911)

The main theorem of this paper gives a sufficient condition for a class \(A\) of ordinals to be \(\Delta_1\)-definable from a real, in a class-generic extension of \(L\). The condition demands that \(A\) be well-behaved with respect to certain condensation arguments. By way of an application the class or ordinals of cofinality \(\omega\) is shown to be \(\Delta_1\)-definable from a real that lies strictly below \(0^\#\).