Nondefinability of Rings of Integers in Most Algebraic Fields

IF 0.6 3区数学 Q2 LOGIC

Notre Dame Journal of Formal Logic Pub Date : 2020-11-29 DOI:10.1215/00294527-2021-0029

Philip Dittmann, Arno Fehm

引用次数: 3

Abstract

We show that the set of algebraic extensions $F$ of $\mathbb{Q}$ in which $\mathbb{Z}$ or the ring of integers $\mathcal{O}_F$ are definable is meager in the set of all algebraic extensions.

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大多数代数域中整数环的不可定义性

证明了$\mathbb{Q}$的代数扩展集$F$，其中$\mathbb{Z}$或整数环$\mathcal{O}_F$是可定义的，在所有代数扩展集合中是最小的。

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

Notre Dame Journal of Formal Logic MATHEMATICS-LOGIC

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Notre Dame Journal of Formal Logic, founded in 1960, aims to publish high quality and original research papers in philosophical logic, mathematical logic, and related areas, including papers of compelling historical interest. The Journal is also willing to selectively publish expository articles on important current topics of interest as well as book reviews.