Independence relations for exponential fields

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2023-08-01 DOI:10.1016/j.apal.2023.103288

Vahagn Aslanyan , Robert Henderson, Mark Kamsma , Jonathan Kirby

引用次数: 0

Abstract

We give four different independence relations on any exponential field. Each is a canonical independence relation on a suitable Abstract Elementary Class of exponential fields, showing that two of these are NSOP₁-like and non-simple, a third is stable, and the fourth is the quasiminimal pregeometry of Zilber's exponential fields, previously known to be stable (and uncountably categorical). We also characterise the fourth independence relation in terms of the third, strong independence.

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指数场的独立关系

我们在任何指数域上给出了四种不同的独立关系。每一个都是一个合适的指数域的抽象初等类上的规范独立关系，表明其中两个是NSOP1样的且不简单的，第三个是稳定的，第四个是Zilber指数域的拟极小预几何，先前已知是稳定的（且是不可数的范畴的）。我们还将第四种独立关系定性为第三种，即强烈的独立性。

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.