Relative and modified relative realizability

Abstract

The notion of Relative Realizability was dened in see also The idea is that instead of doing realizability with one partial combinatory algebra A one uses an inclusion of partial combinatory algebras A A such that there are combinators k s A which also serve as combinators for A the principal point being that A computable functions may also act on data in A that need not be computable Of course this is reminiscent of Turings computability with oracles and Kleenes denition and later papers of a recursive functional of higher type which for example in the case of type has to act on any possibly non recursive function