Sharp Vaught's conjecture for some classes of partial orders

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-01-12 DOI:10.1016/j.apal.2024.103411

Miloš S. Kurilić

引用次数: 0

Abstract

Matatyahu Rubin has shown that a sharp version of Vaught's conjecture, $I (T, ω) \in {0, 1, c}$ , holds for each complete theory of linear order $T$ . We show that the same is true for each complete theory of partial order having a model in the minimal class of partial orders containing the class of linear orders and which is closed under finite products and finite disjoint unions. The same holds for the extension of the class of rooted trees admitting a finite monomorphic decomposition, obtained in the same way. The sharp version of Vaught's conjecture also holds for the theories of trees which are infinite disjoint unions of linear orders.

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某些偏序类的夏普-沃特猜想

马塔提胡-鲁宾（Matatyahu Rubin）已经证明，沃特猜想的一个尖锐版本 I(T,ω)∈{0,1,c} 对于线性阶 T 的每一个完整理论都成立。我们证明，对于在包含线性阶类的最小偏阶类中有一个模型并且在有限乘积和有限不相交联合下是封闭的偏阶类的每一个完整理论也是如此。用同样的方法得到的根树类的扩展也是如此，该类允许有限单态分解。沃特猜想的尖锐版本也适用于线性阶的无限不相交联合的树理论。

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.