不稳定理论中的分界线与Baire-1函数的子类

IF 0.3 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2022-03-09 DOI:10.1007/s00153-022-00816-8

Karim Khanaki

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引用次数: 8

摘要

我们给出了SOP(严格序性质)的一个新的表征，在任何模型的理论公式的行为，而不是不得不看的行为不可分辨的序列在饱和的。本文通过对泛函分析风格中各种概念的刻画，以几种方式改进了Shelah的一个定理，即一个理论具有OP(序性)当且仅当它具有IP(独立性)或SOP。指出了一阶理论中分割线与Baire 1函数子类之间的联系，给出了一阶理论中一些类的新表征和新类。

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Dividing lines in unstable theories and subclasses of Baire 1 functions

We give a new characterization of SOP (the strict order property) in terms of the behaviour of formulas in any model of the theory as opposed to having to look at the behaviour of indiscernible sequences inside saturated ones. We refine a theorem of Shelah, namely a theory has OP (the order property) if and only if it has IP (the independence property) or SOP, in several ways by characterizing various notions in functional analytic style. We point out some connections between dividing lines in first order theories and subclasses of Baire 1 functions, and give new characterizations of some classes and new classes of first order theories.

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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.