Polymorphic Ordinal Notations
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918063787474944 |
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| author | Towsner, Henry |
| author_facet | Towsner, Henry |
| 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 $Π^1_2-CA_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02131 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polymorphic Ordinal Notations Towsner, Henry Logic 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 $Π^1_2-CA_0$. |
| title | Polymorphic Ordinal Notations |
| topic | Logic |
| url | https://arxiv.org/abs/2504.02131 |