Forcing with copies of the Rado and Henson graphs

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.2023.103286

Osvaldo Guzmán , Stevo Todorcevic

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引用次数: 1

Abstract

If $B$ is a relational structure, define $P (B)$ the partial order of all substructures of $B$ that are isomorphic to it. Improving a result of Kurilić and the second author, we prove that if $R$ is the random graph, then $P (R)$ is forcing equivalent to $S ⁎ \dot{R}$ , where $S$ is Sacks forcing and $\dot{R}$ is an ω-distributive forcing that is not forcing equivalent to a σ-closed one. We also prove that ${P (H}_{3})$ is forcing equivalent to a σ-closed forcing, where $H_{3}$ is the generic triangle-free graph.

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用Rado和Henson图形的拷贝强迫

如果B是关系结构，则定义P（B）为同构于它的B的所有子结构的偏序。改进Kurilić和第二作者的结果，我们证明了如果R是随机图，则P（R）是等价于S R的强迫，其中S是萨克斯强迫，R是不等价于σ-闭强迫的ω-分布强迫。我们还证明了P（H3）是等价于σ-闭强迫的强迫，其中H3是一般的无三角形图。

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.