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Extensions of Scott's Graph Model and Kleene's Second Algebra
Jaap van Oosten, Niels Voorneveld
We use a way to extend partial combinatory algebras (pcas) by forcing them to represent certain functions. In the case of Scott's Graph model, equality is computable relative to th…
Effective Operations of Type 2 in Pcas
Eric Faber, Jaap van Oosten
We exhibit a way of "forcing a functional to be an effective operation" for arbitrary partial combinatory algebras (pcas). This gives a method of defining new pcas from old ones fo…
More on Geometric Morphisms between Realizability Toposes
Eric Faber, Jaap van Oosten
Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the {\e…
Basic Subtoposes of the Effective Topos
Sori Lee, Jaap van Oosten
We employ a new tool (sights) to investigate local operators in the Effective Topos. A number of new such local operators is analyzed using this machinery. Moreover, we investigate…