{"title":"Vector spaces with a union of independent subspaces","authors":"Alessandro Berarducci, Marcello Mamino, Rosario Mennuni","doi":"10.1007/s00153-024-00906-9","DOIUrl":null,"url":null,"abstract":"<div><p>We study the theory of <i>K</i>-vector spaces with a predicate for the union <i>X</i> of an infinite family of independent subspaces. We show that if <i>K</i> is infinite then the theory is complete and admits quantifier elimination in the language of <i>K</i>-vector spaces with predicates for the <i>n</i>-fold sums of <i>X</i> with itself. If <i>K</i> is finite this is no longer true, but we still have that a natural completion is near-model-complete.\n</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-024-00906-9.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00153-024-00906-9","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 study the theory of K-vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite then the theory is complete and admits quantifier elimination in the language of K-vector spaces with predicates for the n-fold sums of X with itself. If K is finite this is no longer true, but we still have that a natural completion is near-model-complete.
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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