Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence
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| Format: | Preprint |
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2025
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| _version_ | 1866916954209517568 |
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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 recursive theory that completely axiomatizes the structure $\langle \mathbb{Z},<, +,f,0\rangle$ where $f$ is the function that maps each $x$ to the integer part of $φx $, with $φ$ the golden ratio. We prove that our axiomatization is model-complete in a language expanded with a function which we which we refer as the Fibonacci floor function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_02303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence Khani, Mohsen Valizadeh, Ali N. Zarei, Afshin Logic 03B25, 03C10, 11U09, 11U05 F.4.1 We introduce a recursive theory that completely axiomatizes the structure $\langle \mathbb{Z},<, +,f,0\rangle$ where $f$ is the function that maps each $x$ to the integer part of $φx $, with $φ$ the golden ratio. We prove that our axiomatization is model-complete in a language expanded with a function which we which we refer as the Fibonacci floor function. |
| title | Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence |
| topic | Logic 03B25, 03C10, 11U09, 11U05 F.4.1 |
| url | https://arxiv.org/abs/2508.02303 |