Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866911210078732288 |
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| author | Khani, Mohsen Valizadeh, Ali N. Zarei, Afshin |
| author_facet | Khani, Mohsen Valizadeh, Ali N. Zarei, Afshin |
| contents | We introduce a model-complete theory which completely axiomatizes the structure $Z_α=(Z, +, 0, 1, f)$ where $f : x \to \lfloorα x \rfloor $ is a unary function with $α$ a fixed transcendental number. When $α$ is computable, our theory is recursively enumerable, and hence decidable as a result of completeness. Therefore, this result fits into the more general theme of adding traces of multiplication to integers without losing decidability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_01673 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence Khani, Mohsen Valizadeh, Ali N. Zarei, Afshin Logic Primary 03B25, Secondary 03C10, 11U09, 11U05 We introduce a model-complete theory which completely axiomatizes the structure $Z_α=(Z, +, 0, 1, f)$ where $f : x \to \lfloorα x \rfloor $ is a unary function with $α$ a fixed transcendental number. When $α$ is computable, our theory is recursively enumerable, and hence decidable as a result of completeness. Therefore, this result fits into the more general theme of adding traces of multiplication to integers without losing decidability. |
| title | Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence |
| topic | Logic Primary 03B25, Secondary 03C10, 11U09, 11U05 |
| url | https://arxiv.org/abs/2110.01673 |