On axiom schemata applicable to the formulae with \(\epsilon\)-symbols (Q2639839)

L is a language for the first order predicate calculus and P is a new predicate symbol not occurring in L. An L(P) formula A(P) is called an L- schema, and for a language \(L'\), \(A(L'\)-formulae) stands for the set of formulae of the form A(\(\lambda\) xB(x)) where B(a) is an \(L'\)-formula. T is a set of L-formulae. The author gives a syntactic condition on A(P) such that if \(T+A(L\)-formulae) is consistent and satisfies a condition which the author calls S-rich, then \(T+A(L(\epsilon)\)-formulae) is consistent in the \(\epsilon\)-calculus.