Polymorphic Ordinal Notations
Logic
2025-06-23 v2
Abstract
We give an alternative presentation of the ordinal notation at the strength of which allows the "uncountable" notation 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 .
Keywords
Cite
@article{arxiv.2504.02131,
title = {Polymorphic Ordinal Notations},
author = {Henry Towsner},
journal= {arXiv preprint arXiv:2504.02131},
year = {2025}
}