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arXiv · 2009.12172

Realisability for Infinitary Intuitionistic Set Theory

Merlin Carl·Lorenzo Galeotti·Robert Passmann
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Abstract

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 sound with respect to certain systems of infinitary intuitionistic logic, and that all axioms of infinitary Kripke-Platek set theory are realised. Finally, we use a variant of our notion of realisability to show that the propositional admissible rules of (finitary) intuitionistic Kripke-Platek set theory are exactly the admissible rules of intuitionistic propositional logic.

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Merlin Carl, Lorenzo Galeotti, Robert Passmann. 2020-09-25. Realisability for Infinitary Intuitionistic Set Theory. https://arxiv.org/abs/2009.12172

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