具有 $$\omega $$ 稳定理论的强可构造模型类的塔尔斯基-林登鲍姆代数

IF 0.3 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2024-06-08 DOI:10.1007/s00153-024-00927-4

Mikhail Peretyat’kin

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引用次数: 0

摘要

我们研究了一类具有$\omega $ -稳定理论的强可构造模型。证明了该类的Tarski-Lindenbaum代数是一个布尔$\Sigma ^1_1$代数，其可计算的超滤子在所有超滤子的集合中形成一个密集子集；而且，这个代数对于所有布尔$\Sigma ^1_1$ -代数都是泛的。给出了具有$\omega $ -稳定理论的所有强可构造模型类的Tarski-Lindenbaum代数的一个表征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$The Tarski–Lindenbaum algebra of the class of strongly constructivizable models with $\omega $-stable theories$

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The Tarski–Lindenbaum algebra of the class of strongly constructivizable models with $\omega $-stable theories

We study the class of all strongly constructivizable models having $\omega $-stable theories in a fixed finite rich signature. It is proved that the Tarski–Lindenbaum algebra of this class considered together with a Gödel numbering of the sentences is a Boolean $\Sigma ^1_1$-algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of all Boolean $\Sigma ^1_1$-algebras. This gives a characterization to the Tarski-Lindenbaum algebra of the class of all strongly constructivizable models with $\omega $-stable 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.