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arXiv · 2508.02303

Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence

Mohsen Khani·Ali N. Valizadeh·Afshin Zarei
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Abstract

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 $\varphi x $, with $\varphi$ 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.

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Mohsen Khani, Ali N. Valizadeh, Afshin Zarei. 2025-08-04. Fibonacci Numbers and Model-Complete Axiomatization of Presburger Arithmetic Expanded with a Beatty Sequence. https://arxiv.org/abs/2508.02303

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