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Logics and Admissible Rules of Constructive Set Theories
Rosalie Iemhoff, Robert Passmann
We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the log…
The first-order logic of CZF is intuitionistic first-order logic
Robert Passmann
We prove that the first-order logic of CZF is intuitionistic first-order logic. To do so, we introduce a new model of transfinite computation (Set Register Machines) and combine th…
Converse extensionality and apartness
Benno van den Berg, Robert Passmann
In this paper we try to find a computational interpretation for a strong form of extensionality, which we call "converse extensionality". Converse extensionality principles, which…
Randomising Realisability
Merlin Carl, Lorenzo Galeotti, Robert Passmann
We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positiv…
Realisability for Infinitary Intuitionistic Set Theory
Merlin Carl, Lorenzo Galeotti, Robert Passmann
We introduce a realisability semantics for infinitary intuitionistic set theory that is based on Ordinal Turing Machines (OTMs). We show that our notion of OTM-realisability is sou…
Logics of Intuitionistic Kripke-Platek Set Theory
Rosalie Iemhoff, Robert Passmann
We investigate the logical structure of intuitionistic Kripke-Platek set theory IKP, and show that the first-order logic of IKP is intuitionistic first-order logic IQC.
De Jongh's Theorem for Intuitionistic Zermelo-Fraenkel Set Theory
Robert Passmann
We prove that the propositional logic of intuitionistic set theory IZF is intuitionistic propositional logic IPC. More generally, we show that IZF has the de Jongh property with re…