用一个函数扩展的整数加法结构的模型完备性和可判定性的比蒂序列

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-07-06 DOI:10.1016/j.apal.2024.103493

引用次数: 0

摘要

我们引入了一个模型完备的理论，它完全公理化了结构 Zα=〈Z,+,0,1,f〉，其中 f:x↦⌊αx⌋ 是一个一元函数，α 是一个固定的超越数。此外，我们还证明了 Zα 的可判定性等同于 α 的可计算性。这一结果与在不丧失可判定性的前提下为整数添加乘法踪迹这一更普遍的主题相吻合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Model-completeness and decidability of the additive structure of integers expanded with a function for a Beatty sequence

We introduce a model-complete theory which completely axiomatizes the structure $Z_{α} = 〈 Z, +, 0, 1, f 〉$ where $f : x \mapsto ⌊ α x ⌋$ is a unary function with α a fixed transcendental number. Moreover, we show that decidability of $Z_{α}$ is equivalent to computability of α. This result fits into the more general theme of adding traces of multiplication to integers without losing decidability.

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.