Recognizable Realizability

Merlin Carl

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arXiv · 2408.07030

Recognizable Realizability

Merlin Carl

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Abstract

We introduce a notion of realizability with ordinal Turing machines based on recognizability rather than computability, i.e., the ability to uniquely identify an object. We show that the arising concept of $r$-realizabilty has the property that all axioms of Kripke-Platek set theory are $r$-realizable and that the set of $r$-realizable statements is closed under intuitionistic provability.

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Merlin Carl. 2024-08-13. Recognizable Realizability. https://arxiv.org/abs/2408.07030

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