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arXiv · 2312.13757

On Non-Standard Models of B\"uchi Arithmetics

Alexander Zapryagaev
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Abstract

B\"uchi arithmetics $\mathop{\mathbf{BA}}\nolimits_n$, $n\ge 2$, are extensions of Presburger arithmetic with an unary functional symbol $V_n(x)$ denoting the largest power of $n$ that divides $x$. We explore the structure of non-standard models of B\"uchi arithmetics and construct an example of a countable non-standard model of $\mathop{\mathbf{BA}}\nolimits_2$.

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Alexander Zapryagaev. 2023-12-21. On Non-Standard Models of B\"uchi Arithmetics. https://arxiv.org/abs/2312.13757

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