On classification of continuous first order theories

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2026-07-01 Epub Date: 2026-02-02 DOI:10.1016/j.apal.2026.103729

Karim Khanaki

引用次数: 0

Abstract

We present several new characterizations of IP (the independence property) and SOP (the strict order property) for continuous first-order logic and explore their connections to functional analysis and Banach space theory. Furthermore, we propose new dividing lines for unstable theories by examining subclasses of Baire-1 functions. We also explain why one should not expect a perfect analogue of Shelah's theorem—namely, that a theory is unstable if and only if it has IP or SOP—to hold for real-valued logics, particularly in the context of continuous logic.

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关于连续一阶理论的分类

给出了连续一阶逻辑的独立性和严格序性的几个新特征，并探讨了它们与泛函分析和Banach空间理论的联系。此外，我们通过检验Baire-1函数的子类，提出了不稳定理论的新分界线。我们也解释了为什么我们不应该期待一个完美的类似于Shelah定理——也就是说，一个理论是不稳定的当且仅当它有IP或sop——对于实值逻辑，特别是在连续逻辑的背景下。

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.