{"title":"Sharp Vaught's conjecture for some classes of partial orders","authors":"Miloš S. Kurilić","doi":"10.1016/j.apal.2024.103411","DOIUrl":null,"url":null,"abstract":"<div><p>Matatyahu Rubin has shown that a sharp version of Vaught's conjecture, <span><math><mi>I</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>ω</mi><mo>)</mo><mo>∈</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mi>c</mi><mo>}</mo></math></span>, holds for each complete theory of linear order <span><math><mi>T</mi></math></span>. 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.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 4","pages":"Article 103411"},"PeriodicalIF":0.6000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Logic","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168007224000083","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0
Abstract
Matatyahu Rubin has shown that a sharp version of Vaught's conjecture, , holds for each complete theory of linear order . 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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
