Recognizable Realizability
Logic
2024-08-14 v1
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 -realizabilty has the property that all axioms of Kripke-Platek set theory are -realizable and that the set of -realizable statements is closed under intuitionistic provability.
Keywords
Cite
@article{arxiv.2408.07030,
title = {Recognizable Realizability},
author = {Merlin Carl},
journal= {arXiv preprint arXiv:2408.07030},
year = {2024}
}