a1 Faculty of Mathematics and Computer Science, Catholic University Nijmegen, Toernooiveld 1, 6525 ED, The Netherlands (e-mail: email@example.com)
Let ψ be a partial recursive function (of one argument) with λ-defining term FΛ°. This means
These four possibilities will be covered by one ‘master’ result of Statman which is based on the ‘Anti Diagonal Normalization Theorem’ of Visser (1980). That ingenious theorem about precomplete numerations of Ershov is a powerful tool with applications in recursion theory, metamathematics of arithmetic and lambda calculus.