Equational theory of ordinals with addition and left multiplication by $ω$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909677829226496 |
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| author | Choffrut, Christian |
| author_facet | Choffrut, Christian |
| contents | We show that the equational theory of the structure $\langle ω^ω: (x,y)\mapsto x+y, x\mapsto ωx \rangle $ is finitely axiomatizable and give a simple axiom schema when the domain is the set of transfinite ordinals. We give an algorithm that given a pair of terms $(E,F)$ decides in linear time with respect of their common length whether or not $E=F$ is a consequence of the axioms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equational theory of ordinals with addition and left multiplication by $ω$ Choffrut, Christian Logic We show that the equational theory of the structure $\langle ω^ω: (x,y)\mapsto x+y, x\mapsto ωx \rangle $ is finitely axiomatizable and give a simple axiom schema when the domain is the set of transfinite ordinals. We give an algorithm that given a pair of terms $(E,F)$ decides in linear time with respect of their common length whether or not $E=F$ is a consequence of the axioms. |
| title | Equational theory of ordinals with addition and left multiplication by $ω$ |
| topic | Logic |
| url | https://arxiv.org/abs/2404.13661 |