Joyal and Moerdijk have shown that realizability toposes over partial combinatory algebras (pca) host classes of small maps giving rise to initial ZF-algebras providing models of intuitionistic Zermelo–Fraenkel set theory. Here we show that this can be extended to a much wider class of realizability toposes. For this purpose we first show this result for nested realizability toposes induced by a pca together with a sub-pca and then show that it is preserved by restriction to subtoposes.
Models of Intuitionistic Set Theory in Subtoposes of Nested Realizability Toposes
MASCHIO, SAMUELE;
2015
Abstract
Joyal and Moerdijk have shown that realizability toposes over partial combinatory algebras (pca) host classes of small maps giving rise to initial ZF-algebras providing models of intuitionistic Zermelo–Fraenkel set theory. Here we show that this can be extended to a much wider class of realizability toposes. For this purpose we first show this result for nested realizability toposes induced by a pca together with a sub-pca and then show that it is preserved by restriction to subtoposes.File in questo prodotto:
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