1 citations · 1 across the 4 of their papers we have counts for
4 papers
Classical and Relative Realizability
Jaap van Oosten, Tingxiang Zou
We show that every abstract Krivine structure in the sense of Streicher can be obtained, up to equivalence of the resulting tripos, from a filtered opca (A,A') and a subobject of 1…
Realizability with a Local Operator of A.M. Pitts
Jaap van Oosten
We study a notion of realizability with a local operator J which was first considered by A.M. Pitts in his thesis. Using the Suslin-Kleene theorem, we show that the representable f…
Partial Combinatory Algebras of Functions
Jaap van Oosten
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures a…
A general form of relative recursion
Jaap van Oosten
For every partial combinatory algebra (pca) and every partial endofunction on , a pca is constructed such that in , the function is representable by an elem…