Countable ordered groups and Weihrauch reducibility

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-07-25 DOI:10.1016/j.apal.2025.103644

Ang Li

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引用次数: 0

Abstract

This paper continues to study the connection between reverse mathematics and Weihrauch reducibility. In particular, we study the problems formed from Maltsev's theorem [11] on the order types of countable ordered groups. Solomon [14] showed that the theorem is equivalent to

Π_{1}^{1}

C A_{0}

, the strongest of the big five subsystems of second order arithmetic. We show that the strength of the theorem comes from having a dense linear order without endpoints in its order type. Then, we show that for the related Weihrauch problem to be strong enough to be equivalent to

\hat{WF}

(the analog problem of

Π_{1}^{1}

C A_{0}

), an order-preserving function is necessary in the output. Without the order-preserving function, the problems are very much to the side compared to analog problems of the big five.

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可数有序群与Weihrauch可约性

本文继续研究逆向数学与魏氏约化性之间的联系。特别地，我们研究了由马尔采夫定理[11]形成的关于可数有序群的序型问题。Solomon[14]证明了该定理等价于二阶算法五大子系统中最强的Π11-CA0。我们证明了定理的强度来自于在其阶型中有一个没有端点的密集线性阶。然后，我们证明了为了使相关的Weihrauch问题足够强而等价于WF - （Π11-CA0的模拟问题），输出中必须有一个保序函数。如果没有保序函数，这些问题与五大模拟问题相比就显得微不足道了。

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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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.