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• W2990164068 abstract "Independence of premise principles play an important role in characterizing the modified realizability and the Dialectica interpretations. In this paper we show that a great many intuitionistic set theories are closed under the corresponding independence of premise rule for finite types over $mathbb{N}$. It is also shown that the existence property (or existential definability property) holds for statements of the form $neg Ato exists x^{sigma} F(x^{sigma})$, where the variable $x^{sigma}$ ranges over a finite type $sigma$. This applies in particular to Constructive Zermelo-Fraenkel Set Theory (CZF) and Intuitionistic Zermelo-Fraenkel Set Theory (IZF), two systems known not to have the general existence property. On the technical side, the paper uses the method of realizability with truth from [21] and [8] with the underlying partial combinatory algebra (pca) chosen among the total ones. A particular instance of the latter is provided by the substructure of the graph model formed by the semi computable subsets of $mathbb{N}$, which has the advantage that it forms a set pca even in proof-theoretically weak set theories such as CZF." @default.
• W2990164068 created "2019-12-05" @default.
• W2990164068 creator A5002536453 @default.
• W2990164068 creator A5011325191 @default.
• W2990164068 date "2019-11-19" @default.
• W2990164068 modified "2023-09-23" @default.
• W2990164068 title "The independence of premise rule in intuitionistic set theories" @default.
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