English

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 rr-realizabilty has the property that all axioms of Kripke-Platek set theory are rr-realizable and that the set of rr-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}
}