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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.02131 |
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Table of Contents:
- We give an alternative presentation of the ordinal notation at the strength of $Π^1_1-CA_0$ 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 $Π^1_2-CA_0$.