3 papers
math.LO2022
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…
math.LO2021
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…
math.LO2019
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…