嵌套可实现性拓扑子拓扑中的直觉集合论模型
Models of Intuitionistic Set Theory in Subtoposes of Nested Realizability Toposes
摘要：
每一个PCA $\mathcal{A}$和subPCA $\mathcal{A}_\#$，我们关联的嵌套可实现拓扑$\mathsf{RT}(\mathcal{A},\mathcal{A}_\#)$内，我们确定一类小地图$\mathcal{S}$引起的模型内的直觉集合论$\mathsf{RT}(\mathcal{A},\mathcal{A}_\#)$。对于这样一个嵌套的可实现拓扑的每个子拓扑$\mathcal{E}$，我们在$\mathcal{E}$中构造一个小映射的诱导类$\mathcal{S_E}$，从而在$\mathcal{E}$中产生一个直觉集合论模型。这包括相对可实现性toposes，修改的相对可实现性toposes，修改的可实现性topos和范登伯格最近的Herbrand topos。
英文摘要：
With every pca $\mathcal{A}$ and subpca $\mathcal{A}_\#$ we associate the nested realizability topos $\mathsf{RT}(\mathcal{A},\mathcal{A}_\#)$ within which we identify a class of small maps $\mathcal{S}$ giving rise to a model of intuitionistic set theory within $\mathsf{RT}(\mathcal{A},\mathcal{A}_\#)$. For every subtopos $\mathcal{E}$ of such a nested realizability topos we construct an induced class $\mathcal{S_E}$ of small maps in $\mathcal{E}$ giving rise to a model of intuitionistic set theory within $\mathcal{E}$. This covers relative realizability toposes, modified relative realizability toposes, the modified realizability topos and van den Berg's recent Herbrand topos.
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