 The weak continuity axiom has been shown to be consistent, and is often applied in a form that can be justified, namely in the case in which the predicate \(A\) only refers to the values of \(\alpha\), and not to the higher order properties that it possibly possesses. The details of the argument will be omitted here, but it contains the same ingredients as the justification of the principle for lawless sequences, and can be found in van Atten and van Dalen 2002.