Jaap van Oosten

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The purpose of this short paper is to sketch the development of a few basic topics in the history of Realizability The number of topics is quite limited and re ects very much my own personal taste biases and prejudices Realizability has over the past years developed into a subject of such dimensions that a comprehensive overview would require a fat book(More)
The purpose of this note is to observe a generalization of the concept “computable in. . . ” to arbitrary partial combinatory algebras. For every partial combinatory algebra (pca) A and every partial endofunction on A, a pca A[f ] is constructed such that in A[f ], the function f is representable by an element; a universal property of the construction is(More)
b) (3 points) Define a new function F ′ by: F ′(0,m, ~y, x) = G(~y,Km(x)) F ′(n+ 1,m, ~y, x) = H(n, F ′(n,m, ~y, x), ~y,Km−̇(n+1)(x)) Recall that Km−̇(n+1) means: the function K applied m−̇(n+1) times. Prove: if n ≤ m then ∀k[F ′(n,m+ k, ~y, x) = F ′(n,m, ~y,Kk(x))] c) (3 points) Prove by induction: F (z, ~y, x) = F ′(z, z, ~y, x) and conclude that F is(More)