论 chi算术中普雷斯伯格算术的解释

IF 0.5 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2023-08-30 DOI:10.1134/S1064562423700655

A. A. Zapryagaev

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引用次数: 1

摘要

b chi算法BAn, \(n \geqslant 2\)，是Presburger算法的扩展，其一元函数符号\({{V}_{n}}(x)\)表示Presburger算法是除x的n的最大幂。BAn中的集合的可定义性等同于它的可识别性，由一个有限自动机接收n进展开的数字。我们考虑了BAn标准模型中的解释，并证明了每个解释都有一个与标准模型同构的内部模型。这回答了a . Visser关于某些弱算术理论本身的解释的问题。

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On Interpretations of Presburger Arithmetic in Büchi Arithmetics

Büchi arithmetics BA_n, \(n \geqslant 2\), are extensions of Presburger arithmetic with an unary functional symbol \({{V}_{n}}(x)\) denoting Presburger arithmetic the largest power of n that divides x. Definability of a set in BA_n is equivalent to its recognizability by a finite automaton receiving numbers in their n-ary expansion. We consider the interpretations of in the standard model of BA_n and show that each such interpretation has an internal model isomorphic to the standard one. This answers a question by A. Visser on the interpretations of certain weak arithmetical theories in themselves.

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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.