2024/08/13 by Merlin Carl, Carl, Merlin
Computer Science · #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2408.07030
openalex publication_date 2024/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.