|کد مقاله||کد نشریه||سال انتشار||مقاله انگلیسی||ترجمه فارسی||نسخه تمام متن|
|4661712||1344860||2015||11 صفحه PDF||ندارد||دانلود کنید|
In  Joyal and Moerdijk have shown that realizability toposes over partial combinatory algebras (pca) host classes of small maps giving rise to initial ZFZF-algebras providing models of intuitionistic Zermelo–Fraenkel set theory IZFIZF. Here we show that this can be extended to a much wider class of realizability toposes as considered in  and .For this purpose we first show this result for nested realizability toposes RT(A,A#)RT(A,A#) induced by a pca AA together with a sub-pca A#A# as considered implicitly in  and then show that it is preserved by restriction to subtoposes. This suffices since all toposes considered in  and  arise as subtoposes of some nested realizability toposes.
Journal: Annals of Pure and Applied Logic - Volume 166, Issue 6, June 2015, Pages 729–739