By taking a closer look at the construction of an Ackermann function we see that between any primitive recursive degree and its Ackermann modification there is a dense chain of primitive recursive degrees.

f " ' f " 2 where Sf := (p-) 1⁄2 (iv) denotes the Schwarzian derivative, and that this result is sharp, as the function f(z) = 1⁄2 log 11 z + z shows. Tile method of the proof does not give all sharp functions. We shall show that the sharp function is essentially unique using another approach implying Nehari's result. This shows furthermore that all convex domains except of parallel strip domai...

Let X be a Turing oracle. A function f(n) is said to be boundedly limit recursive in X if it is the limit of an X-recursive sequence of X-recursive functions f̃(n, s) such that the number of times f̃(n, s) changes is bounded by a recursive function of n. Let us say that X is BLR-low if every function which is boundedly limit recursive in X is boundedly limit recursive in 0. This is a lowness prop...

The creative sets of Post [4] are the recursively enumerable sets whose complements are productive in the sense of Dekker [l]. In [l], Dekker introduces the class of semiproductive sets, which properly includes the class of productive sets. If we define a set to be semicreative if it is recursively enumerable and has a semiproductive complement, we obtain a natural generalization of creative se...

In this note, we prove that having unique head-normal forms is a suucient condition on partial combinatory algebras to be completable. As application, we show that the pca of strongly normalizing CL-terms as well as the pca of natural numbers with partial recursive function application can be extended to total combinatory algebras.

Minimization problems involving @-entropyfunctionals (ageneralization of Boltzmann-Shannon entropy) are studied over a givenset A and a sequence of sets A, and the properties of their optimalsolutions I@,I,. Under certain conditions on the objective functional andthe sets A and A,, it is proven that as n increases to infinity, the optimalsolution I, converges in Llno...