{"title":"Positive indiscernibles","authors":"Mark Kamsma","doi":"10.1007/s00153-024-00928-3","DOIUrl":null,"url":null,"abstract":"<div><p>We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str<span>\\(_0\\)</span>-trees (the reduct of str-trees that forgets the length comparison relation) and arrays. In doing so, we prove stronger versions for basing—rather than locally basing or EM-basing—str-trees on s-trees and str<span>\\(_0\\)</span>-trees on str-trees. As an application we show that a thick positive theory has <i>k</i>-<span>\\(\\mathsf {TP_2}\\)</span> iff it has 2-<span>\\(\\mathsf {TP_2}\\)</span></p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-024-00928-3.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00153-024-00928-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
引用次数: 0
Abstract
We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str\(_0\)-trees (the reduct of str-trees that forgets the length comparison relation) and arrays. In doing so, we prove stronger versions for basing—rather than locally basing or EM-basing—str-trees on s-trees and str\(_0\)-trees on str-trees. As an application we show that a thick positive theory has k-\(\mathsf {TP_2}\) iff it has 2-\(\mathsf {TP_2}\)
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.
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