2025/04/02 by Henry Towsner, Towsner, Henry
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2504.02131
openalex publication_date 2025/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an alternative presentation of the ordinal notation at the strength of Π11-CA0 which allows the "uncountable" notation Ω to be interpreted "polymorphically" - that is, we allow the notation to be interpreted as different cardinals depending on their context. This gives us a way to represent functions on ordinals within our ordinal notation system. We then use this idea to present an ordinal notation system for a system a bit weaker than parameter-free Π12-CA0.