Functoriality of modified realizability

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Abstract

We study the notion of modified realizability topos over an arbitrary Schönfinkel algebra. In particular we show that such toposes are induced by subsets of the algebra which we call right pseudo-ideals, and which generalize the right ideals (or right absorbing sets) previously considered. We also investigate the notion of compatibility with right pseudo-ideals which ensures that quasi-surjective (applicative) morphisms of Schönfinkel algebras yield geometric morphisms between these toposes.

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