# Realisability for Infinitary Intuitionistic Set Theory

@article{Carl2020RealisabilityFI, title={Realisability for Infinitary Intuitionistic Set Theory}, author={Merlin Carl and L. Galeotti and Robert Pa{\ss}mann}, journal={arXiv: Logic}, year={2020} }

We introduce a realisability semantics for infinitary intuitionistic set theory that employs Ordinal Turing Machines (OTMs) as realisers. We show that our notion of OTM-realisability is sound with respect to certain systems of infinitary intuitionistic logic, and that all axioms of infinitary Kripke-Platek set theory are realised. As an application of our technique, we show that the propositional admissible rules of (finitary) intuitionistic Kripke-Platek set theory are exactly the admissible… Expand

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