Definability in affine logic

IF 0.5 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2025-04-25 DOI:10.1007/s00153-025-00972-7

Seyed-Mohammad Bagheri

引用次数: 0

Abstract

I study definability notions in the framework of affine continuous logic. Some general results concerning types and definable relations in affinely complete theories are proved. If the theory has a first order model, its extremal theory is a complete first order theory and first order definable sets are affinely definable. If it has a compact model, definable sets are exactly the end-sets of definable predicates. As an example, it is proved in the theory of probability algebras that one dimensional definable sets are exactly the intervals [a, b].

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仿射逻辑中的可定义性

在仿射连续逻辑的框架下研究可定义性概念。证明了仿射完备理论中关于类型和可定义关系的一些一般结果。如果理论具有一阶模型，则其极值理论是完全一阶理论，且一阶可定义集是仿射可定义的。如果它有一个紧凑的模型，可定义集就是可定义谓词的端集。作为一个例子，在概率代数理论中证明了一维可定义集合就是区间[a， b]。

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

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.